Question

The curved surface area of a hemisphere is $308m^2.$ Find the volume and the total surface area of hemisphere.

• A. $462m^3,718.667m^2$
• B. $564m^3,432.997m^2$
• C. $718.667m^3,462m^2$
• D. $432.997m^3,564m^2$

Answer 1

The correct option is C $718.667m^3,462m^2$

Curved surface area of a hemisphere
$=2\pi r^2=308m^2$
$\Rightarrow 2\times \frac{22}{7}\times r^2=308$
$\Rightarrow r=7m$

Volume of a hemisphere is given by,

$V=\frac{2}{3}\pi r^3$

$\Rightarrow V=\frac{2}{3}\times \frac{22}{7}\times (7{)}^3$

$\Rightarrow V=\frac{2156}{3}=718.667m^3$

Total Surface Area of a hemisphere is given by,
$TSA=3\pi r^2$
$\Rightarrow TSA=3\times \frac{22}{7}\times (7{)}^2$
$\Rightarrow TSA=462m^2$