A prism has a trapezoid as its base whose area is 140 square centimeters. A cylinder with the same height has a radius of 6 centimeters. How much larger, to the nearest cubic centimeter, is the volume of the prism than the volume of the cylinder?

difference in volume = 26.96h cm³

Step-by-step explanation:

The volume of a prism is the product of the base area and the height. A trapezoid prism has a trapezium as the base shape. Therefore,

volume of a trapezoid prism = area of a trapezium * height

area of the base (trapezoid) = 140 cm²

Volume = 140h

Volume of a cylinder = πr²h

where

r = radius

h = height

volume = πr²h

volume = π * 6² * h

volume = 3.14 * 36 * h

volume = 113.04h

To know how much larger the volume of the prism is than the volume of the cylinder we have to take the difference of the volume.

Recall the height are the same

difference in volume = 140h - 113.04h

difference in volume = 26.96h cm³