# CBSE Solutions for Class 10 English

#### GSEB std 10 science solution for Gujarati check Subject Chapters Wise::

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, Calculate the total surface area of the article when it is ready.

જવાબ : Height of cylinder = 20 cm And diameter = 7 cm and then radius = 3.5 cm Total surface area of article  = lateral surface of cylinder

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Calculate its surface area.

જવાબ :

A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, calculate the cost of painting the toy at the rate of 70 paise per sq cm.

જવાબ :

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Calculate its capacity.

જવાબ : Radius of cylinder = Radius of hemisphere = 10.5 cm Height of cylinder = (14.5 10.5) cm = 4 cm Capacity = Volume of cylinder + Volume of hemisphere

A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, calculate the radius of the ice-cream cone.

જવાબ :

A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm3 and its diameter is 7 cm, calculate the height of the toy.

જવાબ :

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Calculate the total surface area of the toy.

જવાબ :

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Calculate the volume of the solid.

જવાબ :

A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5m, its height of 21 m and the slant height of the cone is 8 m. Find the total surface area of the rocket.

જવાબ : Radius of cone = Radius  of cylinder = 2.5 m Height of cylinder = 21 m Slant height of cone = 8 m Total surface area of the rocket = (curved surface area of cone                                                               + curved surface area of cylinder + area of base)

A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, calculate the area of canvas needed to make the tent.

જવાબ :

A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Calculate the cost of cloth required to make the tent at the rate of Rs.80 per square meter.

જવાબ : Hence, the curved surface area of the tent = 1034 m2 Cost of canvas = Rs.(1034 × 80) = Rs. 82720

A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 in surmounted by a right circular cone of same base radius. Calculate the length of canvas used in making the tent, if the breadth of the canvas is 1.5 m.

જવાબ :

The surface area of a sphere is 2464 cm2. If its radius be doubled, find the surface area of the new sphere.

જવાબ :

If the total surface area of a solid hemisphere is 462 cm2, calculate its volume.

જવાબ :

Two cubes each of volume 27 cm' are joined end to end to form a solid. Calculate the surface area of the resulting cuboid.

જવાબ :

The volume of a hemisphere is 2425.5 cm3 . Calculate its surface area.

જવાબ :

The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, calculate its volume.

જવાબ :

The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2. Calculate the height of the mountain.

જવાબ :

If the volumes of two cones are in the ratio of 1: 4 and their diameters are in the ratio of 4 : 5, calculate the ratio of their heights.

જવાબ :

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Calculate the cost of cloth used at the rate of Rs. 25 per metre.

જવાબ :

The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, calculate its diameter.

જવાબ : Diameter of sphere = 18 cm Radius of copper sphere =  Length of wire = 108 m = 10800 cm                            But the volume of wire = Volume of sphere
Hence the diameter = 2r = (0.3 2) cm = 0.6 cm

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Calculate the length of the wire.

જવાબ : Diameter of sphere = 42 cm Radius of sphere =  Volume of sphere =  Diameter of cylindrical wire = 2.8 cm Radius of cylindrical wire =  Volume of cylindrical wire =                                      Volume of cylindrical wire = volume of sphere Hence length of the wire 63 m.

A solid sphere of radius 3cm is melted and then cast into small spherical balls, each of diameter 0.6 cm. Calculate the number of small balls so obtained.

જવાબ : Radius of sphere = 3 cm Volume of sphere =  Radius of small sphere =  Volume of small sphere =                                    Let number of small balls be n Hence, the number of small balls = 1000.

જવાબ : Volume of sphere (when r = 1 cm) =  =  Volume of sphere (when r = 8 cm) =  =  Let the number of balls = n

A spherical ball of diameter 21 cm is melted and recast into cubes, each of side 1 cm. Calculate the number of cubes so formed.

જવાબ : Diameter of sphere = 21 cm Hence, radius of sphere =  Volume of sphere =  =  Volume of cube = a3 = (1 1 1)  Let number of cubes formed be n Volume of sphere = n Volume of cube Hence, number of cubes is 4851.

A hemisphere of lead of radius 9 cm is cast intoa right circular cone of height 72 cm. Calculate the radius of the base of the cone.

જવાબ : Volume of hemisphere of radius 9 cm                                          Volume of circular cone (height = 72 cm)                                         Volume of cone = Volume of hemisphere Hence radius of the base of the cone = 4.5 cm

A spherical shell of lead whose external and internal diameters are respectively 24 cm and 18 cm, is melted ad recast into a right circular cylinder 37 cm high. Calculate the diameter of the base of the cylinder.

જવાબ : External radius of shell = 12 cm and internal radius = 9 cm Volume of lead in the shell =   Height of cylinder = 37 cm Volume of cylinder =  Hence diameter of the base of the cylinder = 12 cm

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5cm and 2 cm. Calculate the radius of third ball.

જવાબ :  Volume of third ball = Volume of spherical ball volume of 2 small balls

A spherical cannon ball 28 cm in diameter is melted and recast into right circular conical mould, base of which is 35 cm in diameter. Calculate the height of the cone.

જવાબ : Radius of the cannon ball = 14 cm Volume of cannon ball =  Radius of the cone =  Let the height of cone be h cm Volume of cone =                           Hence, height of the cone = 35.84 cm

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Calculate the number of cones so formed.

જવાબ : Radius of the sphere=  Let the number of cones formed be n, then                             Hence, number of cones formed = 504

A hemispherical bowl of internal diameter 30cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 5 cm and height 6 cm. Calculate the number of bottles necessary to empty the bowl.

જવાબ : Inner radius of the bowl = 15 cm Volume of liquid in it =  Radius of each cylindrical bottle = 2.5 cm and its height = 6 cm Volume of each cylindrical bottle                                         Required number of bottles =                                             Hence, bottles required = 60

A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Calculate the Thickness of the wire.

જવાબ :

The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Calculate the height of the cone so formed.

જવાબ : Internal radius = 3 cm and external radius = 5 cm Hence, height of the cone = 4 cm

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Calculate the height of the cylinder.

જવાબ :

A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Calculate the number of balls thus formed.

જવાબ : Radius of the cone = 12 cm and its height = 24 cm Volume of cone =

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Calculate the radius of the resulting sphere.

જવાબ :

A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Calculate the diameter of the sphere.

જવાબ :

The dimensions of a metallic cuboid are 100 cm x 80 cm x 64 cm. It is melted and recast into a cube. Calculate the surface area of the cube.

જવાબ :

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Calculate the area to be painted by each of these colours.

જવાબ : Solution:

The inner diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, calculate the apparent capacity and the actual capacity of the glass.

જવાબ : Solution:

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy, if the total height of the toy is 30 cm.

જવાબ :

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Calculate the cost of painting the total surface area of the solid so formed, at the rate of Rs.5 per 100 sq cm. [Use π = 3.14.]

જવાબ :

From a cubical piece of wood of side 21 cm, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Calculate the surface area and volume of the remaining piece.

જવાબ :

The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Calculate the volume of the solid.

જવાબ :   Height of cylinder= h1 = 6.5 cm Height of cone =  h2 = 6.3 cm Radius of cylinder = radius of cone = radius of hemisphere =  3.5 cm Volume of solid = Volume of cylinder + Volume of cone + Volume of hemisphere

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Calculate the quantity of water it can hold.

જવાબ : Diameter of spherical part of vessel = 21 cm

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8cm and of base radius 6 cm, is hollowed out. Find the total surface area of the remaining solid. Take π = 3.14

જવાબ : Radius of cylinder = 6 cm Height of cylinder = 8 cm   Surface area of cylinder = 2 = 2× 6 × 8

From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Calculate the volume of the remaining solid.

જવાબ :

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Calculate the total surface area of the remaining solid.

જવાબ :

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8cm and of base radius 6 cm, is hollowed out. Find the volume of the remaining solid. Take π = 3.14

જવાબ : Radius of cylinder = 6 cm Height of cylinder = 8 cm   Volume of cylinder                Volume of cone removed

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 21. cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm, Calculate the volume of the water left in the tub.

જવાબ : Radius of cylinder  r1= 5cm And height of cylinder h1= 9.8cm Radius of cone r2 = 2.1 cm And height of cone h2= 4cm Volume of water left in tub = (volume of cylindrical tub – volume of solid)

66 cubic cm of silver is drawn into a wire 1 mm in diameter. Find the length of the wire in metres.

જવાબ :

The volumes of two cubes are in the ratio 8 : 27. Calculate the ratio of their surface areas.

જવાબ :

The volume of a right circular cylinder with its height equal to the radius is 253 . Calculate the height of the cylinder.

જવાબ :

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm3, calculate the radius of the base of the cylinder.

જવાબ :

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Calculate the ratio of their volumes.

જવાબ :

The volume of a cube is 729 cm3. Calculate its surface area.

જવાબ :

A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km/hr. Find the amount of water (in cubic metres) that runs into the sea per minute.

જવાબ :

Calculate cubes of 10 cm edge can be put in a cubical box of 1 m edge?

જવાબ :

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. Calculate the edge of the new cube formed.

જવાબ :

Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Calculate the volume of the resulting cuboid.

જવાબ :

A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Calculate the radius of the base of the cone.

જવાબ :

A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each. Find the no. of spheres are formed.

જવાબ :

Find the no. of lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm x 11 cm x 12 cm

જવાબ :

A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Calculate the number of spherical balls obtained.

જવાબ :

The surface areas of two spheres are in the ratio of 4 : 25. Calculate the ratio of their volumes.

જવાબ :

The curved surface area of a sphere is 5544 cm3. Find its volume.

જવાબ :

The volume of a sphere is 4851 cm3. Calculate its curved surface area.

જવાબ :

A right cylindrical vessel is full of water. Find the no. of right cones having the same radius and height as those of the right cylinder will be needed to store that water.

જવાબ :

A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Find the radius of the base of the cone.

જવાબ :

If the area of the base of a right circular cone is 3850 cm2 and its height is 84 cm, calculate the slant height of the cone.

જવાબ :

### There are No Content Availble For this Chapter

 1 Total Surface Area of Sphere A 36π cm3 2 Volume of Sphere B 27π cm2 3 Total Surface Area of Hemisphere C 36π cm2 4 Volume of Sphere D 27π cm3

જવાબ :

1-C, 2-A, 3-B, 4-D

Cuboid

 1 Total Surface Area A 2h(l+b) + lb 2 Total Surface Area without lid B 2h(l+b) 3 Curved Surface Area C 2(lb + bh + lh) 4 Volume D Lbh

જવાબ :

1-C, 2-A, 3-B, 4-D

Radius = 3cm and Height of cone = 4cm

 1 Total Surface Area A 15π cm2 2 Slant Height B 24π cm2 3 Curved Surface Area C 12π cm3 4 Volume D 5 cm

જવાબ :

1-B, 2-D, 3-A, 4-C

Radius = 2cm and Height of cylinder = 6cm

 1 Total Surface Area A 42π cm3 2 Total Surface Area without lid B 32π cm2 3 Curved Surface Area C 28π cm2 4 Volume D 24π cm2

જવાબ :

1-B, 2-C, 3-D, 4-A

Side of cube =4 cm

 1 Total Surface Area A 64 cm3 2 Total Surface Area without lid B 64 cm2 3 Curved Surface Area C 80 cm2 4 Volume D 96 cm2

જવાબ :

1-D, 2-C, 3-B, 4-A

Length= 2 cm, Height= 3 cm and Bredth=4 cm

 1 Total Surface Area A 36cm2 2 Total Surface Area without lid B 24cm3 3 Curved Surface Area C 44cm2 4 Volume D 52cm2

જવાબ :

1-D, 2-C, 3-A, 4-B

 1 Total Surface Area of Sphere A 3πr2 2 Volume of Sphere B 23πr3 3 Total Surface Area of Hemisphere C 43πr3 4 Volume of Sphere D 4πr2

જવાબ :

1-D, 2-C, 3-A, 4-B

Cone

 1 Total Surface Area A πr(r+l) 2 Volume B πrl 3 Curved Surface Area C 13 πr2h

જવાબ :

1-A, 2-C, 3-B

Cylinder

 1 Total Surface Area A πr2h 2 Total Surface Area without lid B 2πr(h+r) 3 Curved Surface Area C πr(2h+r) 4 Volume D 2πrh

જવાબ :

1-B, 2-C, 3-D, 4-A

Cube

 1 Total Surface Area A 4s2 2 Total Surface Area without lid B 6s2 3 Curved Surface Area C s3 4 Volume D 5s2

જવાબ :

1-B, 2-D, 3-A, 4-C