RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 21. Surface Area and Volume of a Sphere

Subject: Mathematics - Class 9th

Q. No. 8 of Exercise 21.1

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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.


Given, cylinder of same height and radius is placed on the top of a hemisphere.


Also, length of the shape is 7 cm


⇒ r + r = 7


⇒ r = 3.5 cm


Curved surface area of a hemisphere = 2πr2


Curved surface area of a cylinder = 2πr2


Total surface area of the shape = 4πr2


⇒ Total surface area of the shape = 4 × (22/7) × (3.5)2


⇒ Total surface area of the shape = 154 cm2


Chapter Exercises

Exercise 21.1
Exercise 21.2
CCE - Formative Assessment

More Exercise Questions

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.

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