Question

find the diameter of a sphere whose surface area is 152m^2 ​

Answer 1

We know that surface area of a sphere with radius R is given by

$S.A. = 4 \pi { R}^{2}$

Here,

Given that surface area of a sphere is 152 sq.m.

So,

$4 \pi R {}^{2} = 152 \\ \\ \frac{22}{7} \times R {}^{2} = \frac{152}{4} \\ \\ {R}^{2} = 38 \times \frac{7}{22} \\ \\ {R}^{2} = \frac{266}{22} \\ \\ R = \sqrt{ \frac{133}{11} }$

As we know that

Diameter is twice of Radius

So,

$Diameter = 2 \times \sqrt{ \frac{133}{11} } \: \: \: m$