Question

The sum of total surface area of a hemisphere of radius $r$ and the total surface area of a sphere of radius $\frac{r}{2}$ is

• A. $5\pi r^2$
• B. $4\pi r^2$
• C. $3\pi r^2$
• D. $6\pi r^2$

Answer 1

The correct option is B $4\pi r^2$

Given: Radius of the hemisphere = $r$ and, radius of the sphere $=\frac{r}{2}$
∴ TSA of hemisphere + TSA of sphere
$=3\pi r^2+4\pi {\left(\frac{r}{2}\right)}^2$
$=3\pi r^2+\frac{4\pi r^2}{4}$
$=4\pi r^2$
Hence, the correct answer is option (b).