The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 21. Surface Area and Volume of a Sphere

Subject: Mathematics - Class 9^th

Q. No. 11 of Exercise 21.1

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11

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Surface area of a shephe = 4πr²

Ratio of surface areas of spheres = square of ratio of their radius

Given, diameter of the moon is approximately one fourth of the diameter of the earth

∴ r_m = 1/4 × r_e

⇒ r_m : r_e = 1 : 4

Ratio of their surface area = 1 : 16

11

Chapter Exercises

Exercise 21.1

Exercise 21.2

CCE - Formative Assessment

1

Find the Find the surface area of a sphere of radius :
(i) 10.5 cm

(ii) 5.6 cm

(iii) 14 cm

2

Find the surface area of a sphere of diameter :
(i) 14 cm

(ii) 21 cm

(iii) 3.5 cm

3

Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm. (Use π = 3.14)

4

The surface area of a sphere is 5544 cm², find its diameter.

5

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of the plating it on the inside at the rate of Rs. 4 per 100 cm².

6

The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of Rs. 2 per sq. m.

7

Assuming the earth to be a sphere of radius 6370 km, how many square kilometres is area of the land, if three-fourth of the earth’s surface is covered by water?

8

A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area of the shape if the length of the shape is 7 cm.

9

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100 cm².

10

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs. 10 per m².

11

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

12

A hemi-spherical dome of a building needs to be painted. IF the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5 per 100 cm².

13

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in Fig. 21.11. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of a radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm² and black paint cost 5 paise per cm².