Question

A hose dispenses 1,413 cm³ of water every minute into a cone with a radius of 60 cm and a height of 150 cm. How long will it take to fill the cone? Use 3.14 to approximate pi. Enter your answer in the box.

Answer 1

Hm. Have you ever dispensed water from a hose unto a cone? I know I haven’t, but math can give us a good idea of what it would be like — or at least, how long it would take.

We are told that the hose spills 1413 cm^3 of water every minute. We are also told the cone has a height of 150 cm and a radius of 60 cm. So far, so good.

First things first, we need to find out how much water can fit in the cone. That means volume. The volume of a cone is

π • r^2 • (h/3)

Let’s go ahead and plug in (remember we use 3.14 for π)

(3.14) • (60)^2 • (150/3)

The volume of the cone is 565,200 cm^3

Wait, I’m lost. What were we supposed to do again? Oh, right. We needed to find how long it would take for the hose to fill in the cone. Well, if we know the hose dispenses 1413 cm^3 per minute, and there is a total of 565,200 cm^3 the cone can take, we can divide the volume of the cone by the amount the hose dispenses per minute to get the number of minutes it’d take to fill it.

565200/1413

400 minutes. Wow, ok. I wouldn’t want to wait that long. That’s like watching 3 movies!