Question

A cylinder has a radius of (x + 4) units and a height of 7 units.Which answer choices shows the expression that represents the volume of thecvlinder?

Answer 1

C. V = 7x²π + 56xπ + 112π

Step-by-step explanation

The volume of a cylinder is the product of the cylinder's height and its base area. The base is a circle, so the base area is π times the radius squared,

`V=\pi\cdot r^2\cdot h`

In this problem, the radius is r = (x + 4) and the height is 7 units,

`V=\pi\cdot(x+4)^2\cdot7`

Expand the square using the perfect trinomial squared formula,

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

In this case, a = x and b = 4,

`V=\pi\cdot(x^2+8x+16)\cdot7`

And multiply each term by 7π,

`V=7x^2\pi+56x\pi+112\pi`

Hence, the expression that represents the volume is V = 7x²π + 56xπ + 112π.