## RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13D

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13D.

**Other Exercises**

- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13A
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13B
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13C
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13D

**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

Hope given RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13D are helpful to complete your math homework.

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