The volume of a prism is the product of its height and area of its base, v = bh. a rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. which could be the base area and height of the prism?

Expression for Base Area is 16y²  and height of the prism is y² + y + 3.

Step-by-step explanation:

Given: Expression for volume of a prism =

To find: Expression for the Base area and Height of the Prism.

We know that

Volume of a prism = Base Area × height

So we need to factorize given expression of volume into two factors in which 1st is for Base area and 2nd is for Height of the prism.

Take 16y² common from each terms, we get

It is factorized in two factors,

So,

Base Area = 16y²

Height = y² + y + 3

Therefore, Expression for Base Area is 16y²  and height of the prism is y² + y + 3.

To find the height, form a right triangle using the height of the frustum as one leg and the slant height as the hypotenuse. You will need to do a bit of analysis to determine the length of the other leg (using the side lengths of the two bases). Then the Pythagorean Theorem will give you the height you need to calculate the volume of the frustum.