## Chapter 13 Surface Areas and Volumes Ex 13.4

**Question 1.**
**Find the surface area of a sphere of radius**
**(i) 10.5 cm**
**(ii) 5.6 cm**
**(iii) 14 cm**
**Solution:**

(i) We have, r = 105 cm

**Question 2.**
**Find the surface area of a sphere of diameter**
**(i) 14 cm**
**(ii) 21 cm**
**(iii) 3.5 m**
**Solution:**

**Question 3.**
**Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)**
**Solution:**

We have, r = 10 cm

Total surface area of a hemisphere = 3πr^{2}

= 3 x 3.14 x (10)^{2}

= 9.42 x 100

= 942 cm^{2}

**Question 4.** **The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.** **Solution:**

**Question 5.** **A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹16 per 100 cm ^{2}.**

**Solution:**

**Question 6.**
**Find the radius of a sphere whose surface area is 154 cm ^{2}.**

**Solution:**

Surface area of a sphere = 154 cm

^{2}

Hence, the radius of the sphere is 3.5 cm.

**Question 7.**
**The diameter of the Moon is approximately one-fourth of the diameter of the Earth. Find the ratio of their surface areas.**
**Solution:**

Let diameter of the Earth = d_{1}

**Question 8.**
**A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.**
**Solution:**

Outer radius of the bowl = (Inner radius + Thickness)

= ( 5 + 0.25) cm = 5.25 cm

**Question 9.** **A right circular cylinder just encloses a sphere of radius r (see figure). Find** **(i) surface area of the sphere,** **(ii) curved surface area of the cylinder,** **(iii) ratio of the areas obtained in (i) and (ii).** **Solution:**

The radius of the sphere = r

Radius of the cylinder = Radius of the sphere = r

Height of the cylinder = Diameter = 2r

(i) Surface area of the sphere A_{1} = 4πr^{2}

(ii) Curved surface area of the cylinder = 2πrh

A_{2} = 2π x r x 2r

A_{2} = 4πr^{2}

(iii) Required ratio = A_{1} :A_{2} = 4πr^{2 }: 4πr^{2} = 1 : 1