Question

Katherine has a fish tank shaped like a triangular prism in her living room. The triangle that forms the base of the tank has a base of 24 inches and a height of 20 inches. The entire tank is 36 inches tall. What volume of water is needed to fill the tank if the tank is only filled to 6 inches below the top?

Answer 1

`Volume = 7200in^3`

Explanation:

Given

`B = 24` --- base of the tank base

`h = 20` --- height of the tank base

`H = 36` --- height of the tank

Required:

Determine the volume of water needed for 6 inches below the top

First, calculate the area of the tank base.

`Area = (1)/(2)Bh`

`Area = (1)/(2)*24*20`

`Area = 12*20`

`Area = 240`

If the tank is filled 6 inches below the top, this means that the height of the water is H - 6.

So, the volume is:

`Volume = Area * (H - 6)`

Substitute 240 for Area and 36 for H

`Volume = 240 * (36 - 6)`

`Volume = 240 * 30`

`Volume = 7200in^3`