Question

A full can of vegetable broth is 17 cm tall and has a radius of 5 cm. Morgan uses some of the broth to make curry and now the broth left in the can is 12 cm high.Morgan used approximately ___ cubic centimeters of broth.Use 3.14 for pi. Do not round your answer.

Answer 1

Answer: Morgan used aproximately 392.5 cm^3

To solve this, we calculate the voluime of the full can and then subtract the amount of broth remaining

Full can: we use the formula for the volume of a cillinder

$\pi r^2h=\pi(5cm)^2\cdot17\operatorname{cm}=\text{ 1334.5}cm^3$

Where r is the radius of the can and h the height. In this case, we use 17cm becouse the can is full

Remainning broth: again we use the volume of a cillinder, but in this case we use the height of the reamining broth (12 cm)

$\pi r^2h=\pi(5\operatorname{cm})^2\cdot12\operatorname{cm}=942\operatorname{cm}$

Now we do the full can minus the remaining broth:

$1334.5\operatorname{cm}-942\operatorname{cm}=392.5\operatorname{cm}^3$

And thats the amount of broth used