Question

A cylindrical hut $4$ m tall and $7$ m in diameter is surmounted by aright circular cone of semi-vertical angle $45$ ${}^{\circ }$. The volume of air inside the hut is -

• A. $44.9$ m${}^3$
• B. $154$ m${}^3$
• C. $198.9$ m${}^3$
• D. None of these

Answer 1

Answer: (C)

$198.9$ m${}^3$

Total volume $=\pi r^{2}h+\frac{1}{3}\pi r^2{h}^{\prime }$
$=\pi (3.5{)}^2\times 4+\frac{1}{3}\pi (3.5{)}^2(3.5{)}^2$
$=\pi (3.5{)}^2[4+\frac{3.5}{3}]$
$=198.9{\text{m}}^3$