Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2006 · Marks: · Difficulty:
A conical tent is to accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breathe. The height of the cone is
(a)13 m
(b)14 m
(c)15 m
(d)16 m
Answer
Answer (as printed): C
Explanation
Let radius of base $=r$ and height $=h$. Required floor area $=(4 \times 11) \mathrm{m}^{2}=44 \mathrm{m}^{2}$. So, $\pi r^{2}=44$. Required volume $=(20 \times 11) \mathrm{m}^{3}=220 \mathrm{m}^{3}$. $$\text { So, } \frac{1}{3} \pi r^{2} h=220 \Rightarrow \frac{1}{3} \times 44 \times h=220 \Rightarrow h=\frac{220 \times 3}{44}=15 \mathrm{m} .$$