Question

A hollow post is made out of a lightweight aluminum alloy that is 1.5 cm thick. The alloy is folded into the shape of a right rectangular prism measuring 9 cm by 9 cm by 28 cm. Find the total volume of alloy in the post. Round your answer to the nearest hundredth if necessary.

Answer 1

The total volume of the alloy in the hollow post is 278.25 cm³.

Step-by-step explanation:

To find the total volume of the hollow post, we need to calculate the volume of the outer shape and subtract the volume of the inner shape.

The outer shape is a rectangular prism with dimensions 9 cm by 9 cm by 28 cm.

The inner shape is also a rectangular prism with dimensions 8.5 cm by 8.5 cm by 27 cm.

The volume of the outer shape is 9 cm * 9 cm * 28 cm = 2268 cm³, and the volume of the inner shape is 8.5 cm * 8.5 cm * 27 cm = 1989.75 cm³.

Subtracting the volume of the inner shape from the volume of the outer shape, we get 2268 cm³ - 1989.75 cm³ = 278.25 cm³.