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Question

# What will be the diameter of the sphere whose surface area is 616 cm2?

A
7 cm
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B
14 cm
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C
28 cm
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D
142 cm
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Solution

## The correct option is B 14 cmThe figure of a sphere with centre at O and diameter AB can be depicted as follows: It can be clearly observed that the radius is half the diameter, i.e., r=d2, where r is the radius and d is the diameter of sphere. The formula used to calculate the surface area of the sphere is 4πr2. It is given that the surface area is 616 cm2, therefore the radius of sphere can be calculated as Surface area of sphere=4πr2616=4(227)r2r2=6164×722r2=49r=7 Substitute the value of r in the formula r=d2, to obtain the value of diameter of sphere, i.e., 7=d2d=7×2=14 Hence, the diameter of the given sphere is 14 cm.

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