Question

16. Volume of two spheres are in the ratio 64: 27. Find the ratio of their radius.​

Answer 1

Solution

Given :-

• Volume of two spheres are in the ratio 64: 27.

Find :-

• ratio of their radius.

Explanation

Let,

• Radius of first sphere = r
• Radius of second sphere = r'

Using Formula

$\boxed{\underline{\tt{\red{\:Volume_{sphere}\:=\:\dfrac{4\pi\times r^3}{3}}}}}$

Now, Calculate Volume

==> Volume of first sphere = 4πr³/3

And,

==> Volume of second sphere = 4πr'³/3

Take radio of both volume

==> (Volume of first sphere)/(Volume of second sphere) = 64/27

==> (4πr³/3)/(4πr'³/3) = 64/27

==>r³/r'³ = 64/27

==> (r/r')³ = (4/3)³

We Know,

if , a^m = b ^m

Then,

• a = b

so,

==> r/r' = 4/3

Or,

==> r :r' = 4:3

Hence

• Ratio between Radius of first sphere & second sphere be = 4:3

_____________________

Answer 2

Answer:

Ratio between Radius of first sphere & second sphere be = 4:3

Step-by-step explanation:

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