Question

The volume of two spheres is in the ratio $64:27$ and the sum of their radii is $7cm$. The difference in their total surface areas is

• A. $38{cm}^2$
• B. $58{cm}^2$
• C. $78{cm}^2$
• D. $88{cm}^2$

Answer 1

The correct option is D $88{cm}^2$

Ration is volume of two spheres $=\frac{64}{27}$

$\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}=\frac{64}{27}(\frac{r_1}{r_2}{)}^3=(\frac{4}{3}{)}^3{r}_1=4r_2=3$

Difference in surface area

$4\pi r_1^{2}4\pi 4_2^2=4\pi (r_1^2-r_2^2)=4\pi (4^2-3^2)=4\pi (16-9)=4\pi \left(7\right)=28\pi =28\times \frac{22}{7}=88c{m}^2$