Question

If the volume and the surface area of a sphere are numerically equal, then find the radius of the sphere.

Answer 1

VOLUME: Space occupied by an object is called a volume of that particular object. Volume is always measured in cube unit.

SURFACE AREA: Surface area of a solid body is the area of all of it surfaces together and it is always measured in square unit.

SPHERE:
A sphere is a solid generated by the revolution of a semicircle about its diameter.

Volume of sphere: (4/3)πr³
Surface area of sphere: 4πr²

SOLUTION:

Given:
Volume of the sphere = surface area of a sphere
(4/3)πr³  = 4πr²
(⅓)r³  = r²
r³ = 3 r²
r³ / r² = 3
r = 3 units.

Hence, the radius of the sphere is 3 units.

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Answer 2

volume =surface area
$\frac{4}{3} \pi {r}^{3} = 4\pi {r}^{2} \\ \frac{4}{3} {r}^{3} - 4 {r}^{2} = 0 \\ 4 {r}^{2} ( \frac{r}{3} - 1) = 0 \\ r = 0 \: or \: r = 3 \\ r \: cant \: be \: zero \\ hence \: r = 3$
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