Question

A bottle that contains hand sanitizer is in the shape of a pyramid with a rectangular base. The length of the base is 4 cm, and the height of the bottle is 7 cm. Suppose the volume of the bottle is 140 cm³. Calculate the width of the base of the bottle. Show ALL your work.

Answer 1

Base of the bottle = 15 cm

Explanation:

Let's start by using the formula for the volume of a pyramid:

Volume of a pyramid = (1/3) * Base Area * Height

We know that the volume of the bottle is 140 cm³ and the height of the pyramid is 7 cm. We need to find the width of the base of the pyramid.

Let's first find the area of the rectangular base:

Base Area = Length * Width

We know that the length of the base is 4 cm, but we don't know the width. Let's call the width "w".

Base Area = 4 * w

Base Area = 4w

Now we can substitute the values we know into the formula for the volume of a pyramid:

Volume of a pyramid = (1/3) * Base Area * Height

140 = (1/3) * (4w) * 7

Simplifying the equation:

140 = (4/3) * 7w

140 = 9.333w

w = 15

Therefore, the width of the base of the bottle is 15 cm.