Question

the surface areas of two spheres are in the ratio of 16:25 then their volumes are in the ratio of​

Answer 1

Answer:

64:125

Step-by-step explanation:

4πa²:4πb²=16:25

or, a²:b²=16:25

or,a:b=4:5

Now,

4\3πa³:4\3πb³

=a³:b³

=4³:5³

=64:125

Hope you are satisfied...

Answer 2

Ratio of volume will be 64:125

Step-by-step explanation:

We have given ratio of surface area of spheres is 16:25

Surface area of sphere is given by $A=4\pi r^2$

Let surface area of sphere 1 is $A_1$ and surface area of sphere 2 is $A_2$

So $\frac{A_1}{A_2}=\frac{16}{25}$

$\frac{4\pi r_1^2}{4\pi r_2^2}=\frac{16}{25}$

$\frac{ r_1^2}{ r_2^2}=\frac{16}{25}$

$\frac{ r_1}{ r_2}=\frac{4}{5}$

Volume of the sphere is given by $V=\frac{4}{3}\pi r^3$

So $\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}$

$\frac{V_1}{V_2}=\frac{r_1^3}{r_2^3}=\frac{4^3}{5^3}=\frac{64}{125}$

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Report by Kanya123 18.11.2018

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