Question

The volumes of two hemispheres are in the ratio 686:250. What is the ratio of their radii?


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Answer 1

Answer:

7:5 is the correct ans

Explanation:

keep smiling

Answer 2

$\huge{\mathbb{\red{ANSWER:-}}}$

For two hemispheres :-

Given :-

$\sf{\dfrac{V1}{V2} =\dfrac{686}{250}}$

Let :-

$\sf{radius \: of \: first \: hemisphere = r1}$

$\sf{radius \: of \: second \: hemisphere = r2}$

To Find :-

$\sf{\dfrac{r1}{r2} = ?}$

Using Formula :-

$\sf{\sf\boxed{Volume \: of \: hemisphere =\dfrac{2}{3}\pi r^{3}}}$

Solution :-

$\sf{Volume \: of \: first \: hemisphere =\dfrac{2}{3}\pi (r1)^{3}}$

$\sf{Volume \: of \: second \: hemisphere =\dfrac{2}{3}\pi (r2)^{3}}$

Now ,

$\sf{\dfrac{V1}{V2} =\dfrac{686}{250} =\dfrac{343}{125}}$

$\sf{\dfrac{(r1)^{3}}{(r2)^{3}}=\dfrac{343}{125}}$

$\sf{(\dfrac{r1}{r2})^{3} =\dfrac{7^{3}}{5^{3}}}$

$\sf{(\dfrac{r1}{r2})^{3} =(\dfrac{7}{5})^{3}}$

$\sf{(\dfrac{r1}{r2}) =\dfrac{7}{5}}$

Result :-

$\sf{r1 : r2 = 7 : 5}$

Extra Related Formulas :-

$\sf{1) TSA \: of \: hemisphere =3\pi r^{2}}$

$\sf{2) CSA \: of \: hemisphere =2\pi r^{2}}$