## NCERT solutions for class 9 Maths

**Surface Areas and Volumes**

**Chapter 13 **

**Exercise 13.8**

**EX 13.8 QUESTION 1.**

**Find the volume of a sphere whose radius is**

**(i) 7 cm**

**(ii) 0.63 cm**

**Solution:**

(i) Radius (r) = 7cm

Volume of sphere = πr = x x 7 x 7 x 7 = 4312 / 3 cm^{3} = 1437cm^{3}

Thus, the volume of sphere = 1437cm^{3}

(ii) Radius (r) = 0.63 m

Volume of sphere = πr = x x 0.63 x 0.63 x 0.63 = 1.05 m^{3} (approx.)

Thus, the volume of sphere = 1.05 m^{3} (approx.)

**Ex 13.8 Question 2.**

**Find the amount of water displaced by a solid spherical ball of diameter**

**(i) 28 cm**

**(ii) 0.21 m**

**Solution:**

(i) Radius of the ball (r) cm cm = 14cm

Volume of the spherical ball = πr^{3}

(ii) Radius(r) = 0.21/2 m = 0.105m

Volume of sphere = πr³ = x x 0.105 x 0.105 x 0.105 = 0.004861 m^{3}

Thus, the amount of water displayed = 0.004861 m^{3}.

**Ex 13.8 Question 3.**

**The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm ^{3}?**

**Solution:**

Radius (r) = cm = 2.1cm

Volume of sphere = πr³ = x x 2.1 x 2.1 x 2.1 = 38.808 cm

^{3}

Mass of 1 cm³ = 8.9 g

∴ Mass of 38.808 cm = 8.9 x 38.808 = 345.39 g (approx.)

Thus, the mass of ball = 345.39 g (approx.)

**Ex 13.8 Question 4.**

**The diameter of the Moon is approximately one-fourth of the diameter of the Earth. What fraction of the volume of the Earth is the volume of the Moon?**

**Solution:**

**Ex 13.8 Question 5.**

**How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?**

**Solution:**

Radius of the hemispherical bowl (r) = cm

Thus, the capacity of the bowl = 0.303 litres (approx.)

**Ex 13.8 Question 6.**

**A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.**

**Solution:**

**Ex 13.8 Question 7.**

**Find the volume of a sphere whose surface area is 154 cm ^{2}.**

**Solution:**

**Ex 13.8 Question 8.**

**A dome of a building is in the form of a hemisphere. From inside, it was white washed at the cost of ₹498.96. If the cost of white washing is ₹2.00 per square metre, find the**

**(i) inside surface area of the dome,**

**(ii) volume of the air inside the dome.**

**Solution:**

**Ex 13.8 Question 9.**

**Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’. Find the**

**(i) radius r’ of the new sphere,**

**(ii) ratio of S and S’.**

**Solution:**

(i) Let the radius of a sphere = r and the radius of new sphere = r’.

Volume of solid sphere = πr^{3}

Volume of 27 solid spheres = 27 x [ πr^{3}]

∴ Volume of the new sphere = Volume of 27 solid spheres

Hence, the radius of a new sphere is 3r.

(ii) Surface area of a sphere S = 4πr^{2}

Surface area of a sphere S’ = 4π (r’) = 4π(3r)^{2} = 36πr^{2}

Thus, S : S’ = 1 : 9

**Ex 13.8 Question 10.**

**A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm ^{3}) is needed to fill this capsule?**

**Solution:**

Radius of the spherical capsule (r) = mm = 1.75mm

∴ Volume of the spherical capsule = πr

^{3}

= x x 1.75 x 1.75 x 1.75

= 22.46 mm

^{3}(approx.)