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RD Chapter 21 Surface Areas and Volume of a Sphere Ex 21.1 Solutions

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

Answer - 1 : - In a sphere,
(i) Radius (r) = 10.5 cm
Surface area = 4πr2

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

Answer - 2 : -

(i) Diameter of a sphere = 14 cm
Radius (r) = 14/2 = 7 cm

Question - 3 : - Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm. [Use π = 3.14]

Answer - 3 : -

(i) Radius of hemisphere = 10 cm
∴ Totalsurface area of hemisphere = 2πr2
= 2 x 3.14 x 10 x 10 cm2
= 628 cm2
(ii) Total surface area of solid hemisphere
= 3πr2 = 3 x 3.14 x 10 x 10 cm2
= 942 cm2

Question - 4 : - The surface area of a sphere in 5544 cm2, find the diameter.

Answer - 4 : - Let r be the radius of a sphere, then Surface area =4πr2

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 ₹4 per 100 cm2. [NCERT]

Answer - 5 : - Inner diameter of a hemispherical bowl = 10.5 cm

Question - 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 ₹2 per sq. m.

Answer - 6 : -

Radius of dome (hemispherical) = 63 dm
Area of curved surface

Question - 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?

Answer - 7 : -

Radius of earth (sphere) = 6370 km
Water on the earth = 3/4 % total area

Question - 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 be 7 cm.

Answer - 8 : - Total height of the so formed shape = 7 cm

Question - 9 : - The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Answer - 9 : - Diameter of moon = 1/4 of diameter of earth
Let radius of earth = r km
Then radius of moon = 1/4 r km
Now surface area of earth = 4πr2

Question - 10 : - 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 ₹5 per 100 cm2. [NCERT]

Answer - 10 : - Circumference of the base of dome (r) = 17.6 m

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