Question

If a hemispherical dome has an inner diameter of 28 m, then its volume (in m${}^3$) is:

• A. $6186.60$
• B. $5749.33$
• C. $7099.33$
• D. $7459.33$

Answer 1

The correct option is B $5749.33$

Given that, the inner diameter of a hemispherical dome is $28m$.

To find out: The volume of the dome.

Radius of the hemispherical dome, $r=\frac{28}{2}=14m$

We know that, the volume of a hemisphere of radius $r$ is $\frac{2}{3}\pi r^3$

$\therefore Volume=\frac{2}{3}\times \frac{22}{7}\times 14\times 14\times 14[\because \pi =\frac{22}{7}]$

$\Rightarrow \frac{120736}{21}$

$\therefore Volume=5749.33m^3$

Hence, the volume of the given hemispherical dome is $5749.33m^3$.