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

ANSWER

C. V = 7x²π + 56xπ + 112π

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.