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 m3
B
154 m3
C
198.9 m3
D
None of these

Solution

The correct option is B $$198.9$$ m$$^3$$Total volume $$= \pi r^2 h + \displaystyle \frac{1}{3} \pi r^2 h'$$$$= \pi (3.5)^2 \times 4 + \dfrac{1}{3} \pi (3.5)^2 (3.5)^2$$$$=\pi (3.5)^2 \left [ 4 + \dfrac{3.5}{3} \right ]$$$$=198.9 \ \text{m}^3$$Mathematics

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