Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height, the height being equal to the radius of the circular base. Their total surface areas are in the ratio:

• A. $(\sqrt{2}+1):3:4$
• B. $(\sqrt{3}+1):3:4$
• C. $\sqrt{2}:3:4$
• D. $\sqrt{3}:7:8$

Answer 1

The correct option is A $(\sqrt{2}+1):3:4$

$\pi r(r+l):3\pi r^2:2\pi r(r+h)=\pi \times (1+\sqrt{2}):3\times \pi \times 1:2\times \pi \times 1(1+1)=(\sqrt{2}+1):3:4$