Surface Area of Sphere


 
 
Concept Explanation
 

Surface Area of Sphere

Surface area of a Sphere: The surface area of sphere of radius r is given by

S=4pi r^2 ;sq;units

Illustration: Find the surface area of sphere of radius 7cm.

Solution: We known that the surface area S of a sphere of radius r is given by

small S=4pi r^2 with

Given: r = 7cm

  small S=4times frac{22}{7}times 7times 7

      small =616cm^2

Illustration: 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 Moon's diameter = d

Given: The diameter of the moon is approximately one fourth of the diameter of the Earth

Hence, Earth's diameter = 4d

Let small S_{1} and small S_{2}  denote the surface areas of Moon and Earth respectively.. Then,

small S_{1}=4 pi left ( frac{d}{2} right )^{2}

small S_{2}=4 pi left ( frac{4d}{2} right )^{2}

small frac{S_{1}}{S_{2}}=frac{4;pi left ( frac{d}{2} right )^{2}}{4 pi left ( frac{4d}{2} right )^{2}}

small frac{S_{1}}{S_{2}}=frac{left ( frac{d}{2} right )^{2}}{left ( 2d right )^{2}}

small frac{S_{1}}{S_{2}}=frac{d^{2}}{4}times frac{1}{4d^{2}}

small frac{S_{1}}{S_{2}}= frac{1}{16}

Hence the ratio of their surface areas = 1 : 16

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Find the surface area of sphere of radius 10.5 cm.

Right Option : A
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Explanation
Question : 2

The surface area of a sphere is 5544 sq cm, its diameter is _________________.

Right Option : C
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Explanation
Question : 3

The surface area of a sphere is 1056 sq cm, its diameter is __________________ .

Right Option : C
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Explanation
 
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