Question

The outer curved surface area of hemisphere and sphere are in the ratio of 2:9 find the ratio in their radii

Answer 1

Answer:

2:3

Step-by-step explanation:

CSA of hemisphere = 2πr²                 [r= radius of hemisphere]

CSA of sphere = 4πR²                        [R=radius of sphere]

thus ratio of their CSA= 2:9

∴2/9 = 2πr²/4πR²

2/9= r²/2R²

2/9×2R²=r²

2×2R²=9×r²

4R²=9r²

r²/R²=4/9

r/R=√4/√9

∴r/R=2/3

ratio of the radii of the hemisphere and sphere

r:R=2:3

Answer 2

Answer:

2:3

Step-by-step explanation:

Ratio of the C.S.As = 2:9

Let the radius of the hemisphere be r and the radius of the sphere be R.

Now,

$\frac{2}{9} =\frac{2\pi r^{2}}{4\pi R^{2} } \\\\\(=)\frac{2}{9} = \frac{r^{2} }{2R^{2} } \\\\=) \frac{\sqrt[]{4} }{\sqrt[]{9} } = \frac{r}{R\\} \\\\=) \frac{2}{3} = \frac{r}{R}$

Here, we can see that the ratio is 2:3.

Hence, the ratio of the radii is 2:3.

Thank You...