Question

after receiving the new football jerseys, a schools coach held a contest where students could guess how many tennis balls would fit inside the shipping box. some students remembered that they didnt have to guess, but could use the dimensions to determine the exact number of tennis balls. 7a using the dimensions in the given image, what is the volume of the box? (worth 2 points) your answer 7b what is the volume of the tennis ball if the diameter is 2.75 inches? use 3.14 for pi and round to the nearest hundredth. (worth 2 points) your answer 7c how many tennis balls can fit inside the shipping box? (worth 2 points) your answer

Explanation:

Step1: Calculate volume of box

The box is a rectangular - prism. The volume formula for a rectangular - prism is $V = l\times w\times h$. Given $l = 120$ inches, $w = 35$ inches, and $h = 30$ inches.
$V_{box}=120\times35\times30$
$V_{box}=126000$ cubic inches

Step2: Calculate volume of tennis - ball

The tennis - ball is a sphere. The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Given diameter $d = 2.75$ inches, so radius $r=\frac{d}{2}=\frac{2.75}{2}=1.375$ inches and $\pi = 3.14$.
$V_{ball}=\frac{4}{3}\times3.14\times(1.375)^{3}$
$V_{ball}=\frac{4}{3}\times3.14\times2.6005859375$
$V_{ball}\approx10.89$ cubic inches

Step3: Calculate number of tennis - balls

To find the number of tennis - balls that can fit in the box, divide the volume of the box by the volume of a tennis - ball.
$n=\frac{V_{box}}{V_{ball}}=\frac{126000}{10.89}\approx11570.25$
Since we can't have a fraction of a ball, the number of whole tennis - balls that can fit is 11570.

Answer:

7A. 126000 cubic inches
7B. 10.89 cubic inches
7C. 11570