# Surface Areas and Volumes – Exercise 13.8 – (MATHEMATICS) – 9th Class

**Exercise 13.8**

Assume π =, unless stated otherwiese.

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

(i) 7 cm

(ii) 0.63 m.

### Show Answer

**Sol.** (i) Radius (r) = 7 cm

Volume =

= 1437 cm³

(ii) Volume =

= 1.05 m³ (approx.).

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

**(i) 28 cm**

**(ii) 0.21 m.**

### Show Answer

**Sol.** Volume of water displaced = Volume of solid spherical

(i) Diameter = 28 cm ⇒ Radius = 14 cm.

∴ Volume of water displaced =

= 11498

(ii) Diameter = 0.21 m ⇒ Radius = 0.105 m.

∴ Volume of water displaced =

= 0.004851 m³.

**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 cm³?**

### Show Answer

**Sol.** Diameter of the ball = 4.2 cm.

⇒ Radius of the ball = 2.1 cm.

Volume of the ball =

Mass of the ball = density × volume

= 8.9 × 38.808 g

= 345.39 g (approx.)

**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?**

### Show Answer

**Sol.** Let diameter of the earth = d units.

⇒ Radius of the earth = units.

Diameter of the moon =

⇒ Radius of the moon =

Volume of the earth /Volume of the moon =

Volume of the moon = volume of the earth.

Hence, the volume of the moon is of the volume of the earth.

**5. How many liters milk can a hemispherical bowl of diameter 10.5 cm hold?**

### Show Answer

**Sol.** Volume of the hemisphere =

= 303.19 cm³

So, the capacity of the bowl

= 0.303 *l* (approx.)

**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.**

### Show Answer

**Sol.** Inner radius = 1 m, thickness

= 1 cm = 0.01 m

Outer radius = 1 + 0.01 m

= 1.01 m

Volume of iron used

= 0.06348 m^{3 }(approx)

**7. Find the volume of a sphere whose surface area is 154 cm².**

### Show Answer

**Sol.** Surface area = 154 cm²

Volume of the sphere =

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

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

**(ii) volume of the air inside the dome. Sol. Cost of white washing = 498.96. Rate of white-washing = 2 per sq. m.**

**Sol. Cost of white washing = 498.96. Rate of white-washing = 2 per sq. m.**

### Show Answer

**Sol.** Cost of white-washing = Rs.498.96.

Rate of white-washing = Rs.2 per sq. m.

(i) Inside surface area =

(ii) We have

∴ Volume of the dome =

= 523.m^{3}(approx.)

**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’**

### Show Answer

**Sol.** Total volume of 27 sphere =

(i) Volume of a new sphere = …..(i)

∴

⇒

(ii) Surface area of each of 27 spheres (S) = 4πr² …(a)

Surface area of a new sphere (S’) = 4π(3r)² = 36π² …(b)

From (a) and (la), we get

Hence, S : S’ = 1 : 9.

**10. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?**

### Show Answer

**Sol.** Diameter (d) = 3.5 mm

∴

Medicine needed = Volume of capsule

= 22.46 mm^{3} (approx)