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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