Question

If the surface area of a sphere is equal to the volume of the sphere, then what is the length of its radius?A. 3 unitsB. 2 unitsC. 0.5 unitsD. 1 unit

Answer 1

Given:

That the surface area of a sphere is equal to the volume of the sphere.

`\begin{gathered} \text{The surface area of a sphere is given by:} \\ A=4\pi r^2 \\ \\ \text{The volume of a sphere is given by:} \\ V=(4)/(3)\pi r^3 \end{gathered}`

If area is equal to volume, then;

`\begin{gathered} A=V \\ 4\pi r^2=(4)/(3)\pi r^3 \\ C\text{ ross multiplying,} \\ 4\pi r^2*3=4\pi r^3 \\ 12\pi r^2=4\pi r^3 \\ \text{Dividing both sides by }4\pi r^2\text{ to get the radius,} \\ (12\pi r^2)/(4\pi r^2)=(4\pi r^3)/(4\pi r^2) \\ 3=r \\ r=3\text{units} \end{gathered}`

Therefore, the length of the radius is 3units.

The correct answer is option A.