Question

(v)What is the ratio of sum of volumes of four hemispheres of radius 1m each to the
volume of a sphere of radius 2m?​

Answer 1

Given - Radius of hemisphere - 1 metre.

Radius of sphere - 2 metre.

Find - Ratio of sum of volumes of four hemisphere to the volume of a sphere.

Solution - Volume of hemisphere is calculated by the formula - 2/3*π*r³ while volume of sphere is calculated by the formula - 4/3*π*r³. In both the formula, r represents radius.

Volume of one hemisphere of radius 1 metre - 2/3*π*1³ = 2π/3.

Volume of four such hemispheres - 4*volume of one hemisphere.

Volume of four hemispheres - 8π/3.

Volume of one sphere of radius 2 metre - 4/3*π*2³

Volume of one sphere - 32π/3.

Ratio of volume of four hemispheres to one sphere - (8π/3):(32π/3)

Ratio - 1:4.

Thus, Ratio of volume of four hemispheres to one sphere of given radius is 1:4.