A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula v = pi r^2 h for the volume of a cylinder.

To find the polynomial that best describes the total volume of the cylinder, we need to substitute the given values of the radius and height into the volume formula.

The volume formula for a cylinder is:

V = πr^2h

Substituting the given values, we have:

V = π(4x + 2)^2(5x + 4)

Expanding the square of (4x + 2):

V = π(16x^2 + 16x + 4)(5x + 4)

Multiplying the binomials:

V = π(80x^3 + 96x^2 + 64x + 20x^2 + 24x + 16)

Simplifying:

V = π(80x^3 + 116x^2 + 88x + 16)

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

V = 80πx^3 + 116πx^2 + 88πx + 16π

To find the volume of a cylinder, we use the formula V = πr^2h, where V represents the volume, r is the radius, and h is the height.

In this case, the radius of the cylinder is given as 4x + 2, and the height is given as 5x + 4. We can substitute these values into the formula to find the volume.

V = π(4x + 2)^2(5x + 4)

Now, let's simplify this expression step by step.

First, let's square the term (4x + 2):

V = π(16x^2 + 16x + 4)(5x + 4)

Next, we distribute the terms:

V = π(80x^3 + 80x^2 + 20x + 64x^2 + 64x + 16)

Now, let's combine like terms:

V = π(80x^3 + 144x^2 + 84x + 16)

Finally, we can rewrite the polynomial in standard form by arranging the terms in descending order of exponent:

V = 80πx^3 + 144πx^2 + 84πx + 16π

Therefore, the polynomial in standard form that best describes the total volume of the cylinder is 80πx^3 + 144πx^2 + 84πx + 16π.

YES

Which of the following situations can be represented by the number sentence below?

x ÷ 4 = 7 + y


A. If there are a certain total number of giraffes and zebras in each of 4 exhibits, then there are 7 giraffes and a certain number of zebras in all.


B. If there are a certain total number of eyes inside a giraffe and zebra exhibit, then there are 7 giraffes and a certain number of zebras inside the exhibit.


C. If there are a certain total number of giraffes and zebras in an exhibit, and they each have 4 babies, then there will be 7 giraffes and a certain number of zebras.


D. If there are a certain total number of legs inside a giraffe and zebra exhibit, then there are 7 giraffes and a certain number of zebras inside the exhibit.