Question

A company is selling two different sized medicine balls to a local colleges athletic department the ratio of the diameters 15:11 if the diameter of the smaller ball is 55cm what is the volume of the larger ball? Round the nearest tenth and use 3.14 for pi.

Answer 1

Volume of larger ball = 220,781.3 cubic centimeters

Explanation:

Let's use ratios to solve for the diameter of the larger ball first (let the diameter of larger ball be L)

`(LargerBall)/(SmallerBall)=(15)/(11)=(L)/(55)\\11*L=15*55\\11*L=825\\L=(825)/(11)=75`

So, the diameter of the larger ball is 75 cm. We know radius is half of diameter, so radius of larger ball is (1/2)(75) = 37.5 cm

Ball is in the shape of a sphere, which has a formula for volume as:

`V=(4)/(3)\pi r^3`

where V is the volume and r is the radius

now we simply plug in 37.5 into r and use 3.14 as π:

`V=(4)/(3)\pi r^3\\V=(4)/(3)(3.14)(37.5)^3\\V=220,781.3`