Question 64

The diameter of a sphere is twice the diameter of another sphere, The surface area ofthefirst sphere is equal to the volume of the second sphere, The magnitude of the radius ofthefirst sphereis

Solution

let radius of sphere 1 = r1

radius of sphere 2 = r2

Given, r1 = 2 r2

surface area of sphere 1 = volume of sphere 2

$$4 \pi (r1)^2 = \frac{4}{3} \pi (r2)^3$$

r1 = 2 r2

$$4 \pi (2r2)^2 = \frac{4}{3} \pi (r2)^3$$

$$ 4 = \frac{1}{3} (r2)$$

r2 = 12

r1 = 2 r2 = 2$$\times$$12 = 24

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