Question

A cylinder has a radius of 6x + 4 and a height of 8x + 7. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula = 2ℎ for the volume of a cylinder. a. 288 3 + 636 2 + 464 + 112 b. 288 3 − 636 2 + 464 + 112 c. 288 3 + 636 2 + 464 + 112 d. 288 3 + 636 2 − 464 + 112

Answer 1

So the answer is (c) 288 3 + 636 2 + 464 + 112.

Explanation:

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. We can substitute the given expressions for r and h to get:

V = π(6x + 4)^2(8x + 7)

Expanding the square, we get:

V = π(36x^2 + 48x + 16)(8x + 7)

Multiplying out the terms, we get:

V = π(288x^3 + 444x^2 + 304x + 112)

Simplifying by multiplying the constants together, we get:

V = 288πx^3 + 444πx^2 + 304πx + 112π

Therefore, the polynomial in a standard form that best describes the total volume of the cylinder is:

288πx^3 + 444πx^2 + 304πx + 112π

And since the question asks for the polynomial in standard form, we can also write it as:

288x^3π + 444x^2π + 304xπ + 112π

So the answer is (c) 288 3 + 636 2 + 464 + 112.