Question

A cone, hemisphere and a cylinder stands on equal bases and have the same height, the height being equal to the radius of the circular base, then their whole 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 $(\sqrt{2}+1):3:4$

Surface area of cone$=\pi r^2+\pi rl$

$=\pi r^2+\pi r\sqrt{r^2+r^2}=\pi r^2+\sqrt{2}\pi$

$=(\sqrt{2}+1)\pi r^2$ .........$\left(1\right)$

S.A of hemisphere$=2\pi r^2+\pi r^2=3\pi r^2$ .......$\left(2\right)$

S.A of cylinder$=2\pi rh+2\pi r^2=2\pi r^2+2\pi r^2$

$=4\pi r^2$ .........$\left(3\right)$

Rate$=(\sqrt{2}+1):3:4$.