SURFACE AREA AND VOLUME
EXERCISE 13.4
EXERCISE 13.4
Q 1. Find the surface area of a sphere of radius:
Solution: (i) Here r = 10.5 cm
∴ Surface area of the sphere = 4πr2
Q 2. Find the surface area of a sphere of diameter:
(i) 14 cm (ii) 21 cm
Solution: (i) Here, Diameter = 14 cm
Q 3. Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)
Solution: Here, radius (r) = 10 cm
Q 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: Case I: When radius (r1) = 7 cm
Q 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 Rs. 16 per 100 cm2.
Solution: Inner diameter of the hemisphere = 10.5 m
∵ Curved surface area of a hemisphere = 2πr2
∴ Inner curved surface area of hemispherical bowl
Q 6. Find the radius of a sphere whose surface area is 154 cm2.
Solution: Let the radius of the sphere be ‘r’ cm.
∴ Surface area = 4πr2
⇒ 4πr2 = 154
Thus, the required radius of the sphere is 3.5 cm
Q 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 the radius of the earth = r
∵ Surface area of a sphere = 4πr2
Since, the earth as well as the moon are considered to be spheres.
∴ Surface area of the earth = 4πr2
or [Surface area of the moon] : [Surface area of the earth] = 1 : 16
Thus, the required ratio = 1 : 16
Q 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: Inner radius (r) = 5cm
Thickness = 0.25 cm
∴ Outer radius (R) = [5.00 + 0.25] cm = 5.25 cm
∴ Outer surface area of the bowl = 2πR2
Q 9. A right circular cylinder just encloses a sphere of radius r (see the figure) find
(i) surface area of the sphere,
Solution: (i) For the sphere:
Radius = r
∴ Surface area of the sphere = 4 πr2
(ii) For the right circular cylinder:
∵ Radius of the cylinder = Radius of the sphere
∴ Radius of the cylinder = r
Height of the cylinder = Diameter of the sphere
⇒ Height of the cylinder (h) = 2r
Since, curved surface area of a cylinder = 2πrh = 2πr(2r) = 4πr2
EXERCISE 13.4