Question

If the volumes of two hemispheres are in the ratio 1:27, then determine the ratio of their
radii.

Answer 1

Solution

Given :-

• Ratio of two hemisphere volume = 1:27

Find :-

• Ratio of their radius

Explanation

Using Formula,

$\dag\boxed{\underline{\tt{\red{\:Volume_{hemisphere}\:=\:\dfrac{2\pi\:r^3}{3}}}}}$

Then take ,

• Volume of first hemisphere = 2/3(πr³)
• Volume of second hemisphere = 2/3(πr'³)

Now, write in radio both volume

==> (Volume of first hemisphere)/(Volume of second hemisphere) = 1/27

==> (2/3)(πr³):(2/3)(πr'³) = 1:27

==> (2/3)(πr³)/(2/3)(πr'³) = 1/27

==> r³/r'³ = 1/27

==> (r/r' )³ = (1/27)

==> r/r' = ³√(1/27/

==>r/r' = ³√(1/3)³

==> r/r' = 1/3

Or,

==> r:r' = 1:3

Hence

• Radio of thier radii will. be = 1:3

_____________________