What is the volume of the fish tank in cubic inches?

Question

A rectangular-prism shaped fish tank is 14 inches tall. The perimeter of the base is 96 inches. The length of the base is 3 times the width of the base.

Answer 1

Hi Daniela L.

6048 in³

According to your information, the base of the tank is a rectangle per the given relationship between the Length and Width.

Perimeter of the Base = 96

Perimeter of the Rectangular Base = 2*Width + 2*Length

Area of the Rectangular Base = Width * Length

Volume of a Rectangular Prism = Area of the Base * Height = Bh = V

Volume of a Rectangular Prism = Length*Width*Height = V

Given that the tank is 14 inches tall, let this represent the height, H

H =14

Since volume is Area of the Base times the height also, Length * Width* Height, you will need you need calculate the dimensions of the Rectangular base from the perimeter given for this base

Perimeter = 96

Perimeter of a Rectangle = 2*Width + 2*Length

Given the Length is 3*Width

Let W = Width

Let L = Length = 3*Width = 3*W

Substituting we have:

96 = 2*W + 2*(3W)

Divide both sides of the equation by 2

48 = W + 3W

48 = 4W

Divide both sides by 4

12 = W

L = 3*W = 3*12 = 36

Checking the numbers,

Perimeter of the Rectangular Base is 96

2*12 + 2* 36 = 24 + 72 = 96

Area of the Rectangular. Base is 12 * 36 = 432

Volume of the Rectangular Tank

432 * 14 = 6048 in³

Also

12 * 36 * 14 = 6048 in³

I hope this helps