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

Respuesta :

Given:

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

[tex]\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=\frac{4}{3}\pi r^3 \end{gathered}[/tex]

If area is equal to volume, then;

[tex]\begin{gathered} A=V \\ 4\pi r^2=\frac{4}{3}\pi r^3 \\ C\text{ ross multiplying,} \\ 4\pi r^2\times3=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,} \\ \frac{12\pi r^2}{4\pi r^2}=\frac{4\pi r^3}{4\pi r^2} \\ 3=r \\ r=3\text{units} \end{gathered}[/tex]

Therefore, the length of the radius is 3units.

The correct answer is option A.