Practice | Hashtable

1. A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface will be :

A. $\sqrt{2} : 1$

B. $1 : \sqrt{2}$

C. 2 : 1

D. 1 : 2

Solution:

Let,

\begin{aligned} O P = O Q = O R = r \\ ∴ O R = h = r \end{aligned}

∴ Curved surface area of the hemisphere =

2 π r^{2}

Curved surface area of a cone =

π r l

Where,

\begin{aligned} l = \sqrt{h^{2} + r^{2}} \\ = \sqrt{r^{2} + r^{2}} \\ = r \sqrt{2} \end{aligned}

∴ Required ratio :

\begin{aligned} = \frac{2 π r^{2}}{π r l} \\ = \frac{2 π r^{2}}{π r \times r \sqrt{2}} \\ = \frac{2}{\sqrt{2}} \\ = \frac{2 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} \\ = \frac{2 \sqrt{2}}{2} \\ = \frac{\sqrt{2}}{1} O r \sqrt{2} : 1 \end{aligned}

You must login to add comments. Login now.