## RS Aggarwal Solutions Chapter 13 Volume and Surface Area Ex 13D in PDF for Free Download

Contents

**Question 1.****Find the volume and surface area of a sphere whose radius is :****(i) 3.5 cm (ii) 4.2 cm (iii) 5m****Solution:**

(i) Radius of sphere = 3.5cm

(a) Volume = πr^{3}

**Question 2.****The volume of a sphere is 38808 cm**^{3}** . Find its radius and hence surface area****Solution:**

Let r be the radius of the sphere and volume = 38808 cm^{3}

∴ πr^{3} = 38803

=> x r^{3} = 38803

**Question 3.****Find the surface area of a sphere whose volume is 606.375 m**^{3}**.****Solution:**

Let r be the radius of the sphere

∴ Volume = πr^{3}

**Question 4.****The surface area of a sphere is 394.24 m**^{2}**. Find its radius and volume.****Solution:**

Surface area of a sphere = 394.24 m^{2}

Let r be the radius, then 4πr^{2} = 394.24

**Question 5.****The surface area of a sphere is (576π) cm**^{2}**. Find its volume.****Solution:**

Surface area of sphere = 576π cm^{2}

Let r be the radius, then 4r^{2} = 576π

**Question 6.****The outer diameter of a spherical shell is 12cm and its inner diameter is 8cm. Find the volume of metal contained in the shell. Also, find its outer Surface area.****Solution:**

Outer diameter of shell = 12cm,

Outer radius (R) = = 6cm

and inner diameter = 8cm

**Question 7.****How many lead shots, each 3mm in diameter, can be made from a cuboid with dimensions (12cm x 11cm x 9cm)****Solution:**

Length of cuboid of (l) = 12cm

Breadth (b) = 11cm

and height (h) = 9cm

**Question 8.****How many lead balls, each of radius 1cm, can be made from a sphere of radius 8cm ?****Solution:**

Radius of sphere (r) = 8cm

Volume = πr^{3}

**Question 9.****A solid sphere of radius 3cm is melted and then cast into smaller spherical balls, each of diameter 0.6cm. Find the number of small balls thus obtained.****Solution:**

Radius of solid sphere (R) = 3cm.

Volume = π(R)^{3} = π(3)^{3} cm^{3}

**Question 10.****A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones, each of radius 3.5cm and height 3cm. How many cones are obtained ?****Solution:**

Radius of metallic sphere (R) = 10.5cm

**Question 11.****How many spheres 12cm in diameter can be made from a metallic cylinder of diameter 8cm and height 90cm ?****Solution:**

Diameter of a cylinder = 8cm

Radius (r) = = 4cm

**Question 12.****The diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 2mm. Find the length of the wire.****Solution:**

Diameter of sphere = 6cm

Radius (R) = = 3cm

**Question 13.****The diameter of a copper sphere is 18cm. It is melted and drawn into a long wire of uniform cross section. If the length qf the wire is 108m, find its diameter.****Solution:**

Diameter of sphere = 18cm

Radius (R) = = 9cm.

**Question 14.****A sphere of diameter 15.6cm is melted and cast into a right circular cone of height 31.2 cm. Find the diameter of the base of the cone.****Solution:**

Diameter of the sphere = 15.6 cm

Radius (R) = = 7.8 cm

**Question 15.****A spherical canonball 28cm in diameter is melted and cast into a right circular cone mould, whose base is 35 cm in diameter. Find the height of the cone.****Solution:**

Diameter of the canonball = 28cm

Radius (R) = = 14 cm

**Question 16.****A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.****Solution:**

Given,

Radius of spherical big ball (R) = 3cm

**Question 17.****The radii of two spheres are in the ratio 1 : 2. Find the ratio of their surfaces areas.****Solution:**

Ratio in the radii of two spheres = 1:2

Let radius of smaller sphere = r then,

radius of bigger sphere = 2r

**Question 18.****The surface areas of two spheres are in the ratio 1 : 4. Find the ratio of their volumes.****Solution:**

Let r1 and r2 be the radii of two spheres

**Question 19.****A cylindrical tub of radius 12 cm contains water to a depth of 20cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball ?****Solution:**

Radius of the cylindrical tub = 12cm.

First level of water = 20cm

Raised water level = 6.75cm.

**Question 20.****A cylindrical bucket with base radius 15cm is filled with water up to a height of 20cm. A heavy iron spherical ball of radius9 cm is dropped into the bucket to submerge completely in the water. Find the increase in the level of water.****Solution:**

Radius of the ball (r) = 9cm.

Volume of ball = πr³

**Question 21.****A hemisphere of lead of radius 9cm is cast into a right circular cone of height 72cm. Find the radius of the base of the cone.****Solution:**

Given,

Radius of hemisphere of lead (r) = 9cm.

**Question 22.****A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm . How many bottles are required to empty the bowl?****Solution:**

Given,

Radius of hemispherical bowl (r) = 9cm

**Question 23.****A hollow spherical shell is made of a metal of density 4.5 g per cm³. If its internal and external radii are 8cm and 9cm respectively, find the weight of the shell.****Solution:**

External radius of spherical shell (R) = 9cm

**Question 24.****A hemispherical bowl is made of steel 0.5cm thick. The inside radius of the bowl is 4cm. Find the volume of steel used in making the bowl.****Solution:**

Inner radius (r) = 4 cm

Thickness of steel used = 0.5

## Leave a Reply