Question

The ratio of the radius of two distinct spheres is 3:4. What is the ratio of their respective surface areas?A. 27:64B. 4:3C. 9:16D. 3:4

Answer 1

Given that the ratio of the radius of two distinct spheres is;

$3\colon4$

The surface area of a sphere is;

$A=4\pi\times r^2$

Thus, the surface area of the first sphere is;

$\begin{gathered} A_1=4\pi(3)^2 \\ A_1=36\pi \end{gathered}$

Similarly, the surface area of the second sphere is;

$\begin{gathered} A_2=4\pi(4)^2 \\ _{}A_2=64\pi \end{gathered}$

Hence, the ratio of the surface areas is;

$\frac{A_1}{A_2}=\frac{36\pi}{64\pi}$

Reducing the fraction, we have;

$\begin{gathered} \frac{A_1}{A_2}=\frac{9}{16} \\ A_1\colon A_2=9\colon16 \end{gathered}$

CORRECT OPTION: C