Question

The ratio of the diameters is 15:11. If the diameter of the smaller ball is 55cm, what is the volume of the larger ball? Round to the nearest tenth and use 3.14 for pi

Answer 1

220,781.25 cubic cm

Explanation:

Given ratio of the diameters = 15:11

Let the actual value of of diameters be 15x and 11x to maintain the ratio of 15:11

Given that smaller one has diameter of 55cm

thus 11x = 55cm

x = 55/11 cm = 5

Thus, diameter of larger ball = 15xcm= 15*5cm =75cm.

we know that radius is half of diameter

Radius = diameter/2

Thus radius of larger ball = 75/2 cm = 37.5 cm.

Volume of sphere is given by
`(4/3)\pi r^3`

we know that ball has spherical shape

thus volume of larger ball is calculated as given below

`volume \ of \ ball = (4/3)\pi r^3\\=> volume \ of \ ball = (4/3)*3.14* 37.5^3\\=> volume \ of \ ball = (4/3)*3.14* 37.5^3\\=> volume \ of \ ball = 220,781.25`

Thus, volume of larger ball is 220,781.25 cubic cm