Question

A cylinder has a height h, and a radius (3h-2)

The area of the base is pi (3h-2)^2


The volume of the clinder is V= pi(3h-2)^2h


10. Multiply the polynomials to simplify the expression for the volume:

V=pi(3h-2)^2h by

Answer 1

To simplify the expression for the volume, multiply the polynomials. The final volume expression is V = pi(13h^3-12h^2)h

Step-by-step explanation:

To simplify the expression for the volume, we need to multiply the polynomials. The polynomial we need to multiply is (3h-2)^2h.

Using the distributive property, we can expand (3h-2)^2 to 9h^2-12h+4h^2. Then, multiply this expression by h to get the final volume expression:

V = pi(9h^2-12h+4h^2)h

Simplifying further, we get:

V = pi(13h^3-12h^2)h

Answer 2

`V= 4\pi (9h^2 -12h + 4)`

Step-by-step explanation:

Given

Shape: Cylinder

`Radius = 3h - 2`

`Height = h`

`Base\ Area = \pi (3h - 2)^2`

Required

Simplify the volume

The volume is calculated as:

`Volume = Base\ Area * Height`

Substitute values for Base Area and Height

`V= \pi(3h-2)^2*h`

Expand the bracket

`V= \pi(3h-2)(3h-2)*h`

Open brackets

`V= \pi (9h^2 -6h - 6h + 4) *h`

`V= \pi (9h^2 -12h + 4) *h`

`V= 4\pi (9h^2 -12h + 4)`