Question

What will be the ratio of the radii of two hemispheres, if it is given that ratio of their volume is 27:64?
A) 34
B) 23
C) 35
D) 12

Answer 1

Answer:

Step-by-step explanation:

Answer => B)23

Answer 2

$\bold{GIVEN}$

Let the radius of one hemisphere be r

and other be R.Let there volume be V and v.

Ratio of volume of two hemispheres = 27 : 64

To find ratio of their radiii, place the volumes in the formula where volume of first hemisphere is divided y second hemisphere.

So,

$\boxed{\mathsf{ \dfrac{V}{v} = \dfrac{ \dfrac{2}{3} \times \pi R^{3}}{ \dfrac{2}{3} \times \pi r^{3}}}}$

$\mathsf{ \dfrac{V}{v} = \dfrac{ \cancel{ \dfrac{2}{3} \times \pi} \times R^{3}}{ \cancel{ \dfrac{2}{3} \times \pi} \times r^{3}}}$

$\mathsf{ \dfrac{27}{64} = \dfrac{R^{3}}{r^{3}}}$

$\mathsf{ \dfrac{\sqrt{27}}{\sqrt{64}} = \dfrac{R}{r}}$

$\boxed{\mathsf{ \dfrac{3}{4} = \dfrac{R}{r}}}$

So, the ratio of there radiii is 3 : 4

Therefore, Option A is correct.