Question

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius R as that of the hemisphere. If H is the height of the cone, then write the values of $\frac{H}{R}$.

Answer 1

Answer:

The value of H/R is 2 .

Step-by-step explanation:

Given :  

Radius of hemisphere = radius of cone = R

Height of the cone = H

Volume of hemisphere  = Volume of cone  

[Hemisphere is melted and recast in the shape of cone]

⅔ πR³ = ⅓ πR²H

2R³ = R²H

2R³/R² = H

2R = H

H/R = 2  

The value of H/R = 2  

Hence, the value of H/R is 2 .

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

HELLO!!!!

As,

volume of metallic hemisphere = volume of cone .

Let the radius of both that is hemisphere and the cone be r.

$(2 \div 3)\pi {r}^{3} = (1 \div 3)\pi {r}^{2} h$

$2 {r}^{3} = r {}^{2} h$

$2 {r}^{3} \div {r}^{2} = h$

$2r = h$

Therefore, value of h/r =2

HOPE IT HELPS UHH #CHEERS