Question

The curved surface area of two hemispheres are in the ratio 36:49. Find the ratio of their radii.​

Answer 1

Explanation:

c.s.a. of hemisphere = 2πr^2

Answer 2

Given:

• ratio of their curved surface area = 36:49

To Find:

• ratio of their radii

Solution:

Let the radius of the first circle be x units

and the radius of the second circle be q units

Ratio of Curved surface area = $\frac{\pi {r}^{2} }{2\pi {q}^{2} }$

$\rightarrow \frac{36}{49} = \frac{ {r}^{2} }{ {q}^{2} } \\ \\ \rightarrow \bigg({ \frac{r}{q} \bigg )}^{2} = \frac{36}{49} \\ \\ \rightarrow \frac{r}{q} = \sqrt{ \frac{36}{49} } \\ \\ \rightarrow \boxed{\frac{r}{q} = \frac{6}{7}}$

Therefore, the ratio of their radii is 6:7