Question

A cylinder has a radius of 5x + 2 and a height of 2x + 8 which polynomial in standard form best describes the total volume of the cylinder?

Use the formula V=pi r^2h for the volume of a cylinder.

Answer 1

`V = 50\pi x^3+240\pi x^2+168\pi x+32 \pi`

Explanation:

Volume of cylinder(V) is given by:

`V = \pi r^2h`

where,

r is the radius of the cylinder

h is the height of the cylinder.

As per the statement:

A cylinder has a radius of 5x + 2 and a height of 2x + 8

⇒r = 5x +2 units and h = 2x+8 units

Substitute in [1] we have;

`V = \pi (5x+2)^2 \cdot (2x+8)`

Using the identity rule:

`(a+b)^2 = a^2+b^2+2ab`

⇒
`V = \pi (25x^2+4+20x)(2x+8)`

⇒
`V = \pi (50x^3+8x+40x^2+200x^2+32+160x)`

Combine like terms;

⇒
`V = \pi (50x^3+240x^2+168x+32)`

⇒
`V = 50x^3 \pi+240x^2 \pi+168x \pi+32 \pi`

Therefore, in standard form best describes the total volume of the cylinder is:
`V = 50x^3 \pi+240x^2 \pi+168x \pi+32 \pi`

Answer 2

V = π r² h
V = π ( 5 x + 2 )² · ( 2 x + 8 ) =
= π ( 25 x² + 20 x + 4 ) · ( 2 x + 8 ) =
= π ( 50 x³ + 200 x² + 40 x² + 160 x + 8 x + 32 ) =
= ( 50 x³ + 240 x² + 168 x + 32 ) π