Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A square pond has 2 m sides and is 1 m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, then what would be the volume of earth to be removed?
(a)$(2 \pi-2) \mathrm{m}^{3}$
(b)$(2 \pi-4) \mathrm{m}^{3}$
(c)$(4 \pi-2) \mathrm{m}^{3}$
(d)$(4 \pi-4) \mathrm{m}^{3}$
Answer
Answer (as printed): B
Explanation
Diagonal of the square $=\sqrt{2^{2}+2^{2}} \mathrm{m}=\sqrt{8} \mathrm{m}=2 \sqrt{2} \mathrm{m}$. Diameter of circular pond $=2 \sqrt{2} \mathrm{m}$. Radius of circular pond = $\sqrt{2} \mathrm{m}$. Volume of circular pond $=\left[\pi \times(\sqrt{2})^{2} \times 1\right] \mathrm{m}^{3}=(2 \pi) \mathrm{m}^{3}$. Volume of square pond $=(2 \times 2 \times 1) \mathrm{m}^{3}=4 \mathrm{m}^{3}$. ∴ Volume of earth to be removed $=(2 \pi-4) \mathrm{m}^{3}$.