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…

Question

asked Oct 19, 2020 99.9k views

1 Answer

Joe Dean · Answer 1 · 2020-10-26T10:00:42+0000

Answer:

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:

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