A cylinder has a radius of 4x + 1 and a height of 3x + 4. Write the

polynomial in standard form for the volume of the cylinder. Use the
formula: V = πr^2h. Leave answer in terms of π.

3 answers

We can begin by substituting the given values into the formula:

V = π(4x+1)^2(3x+4)

To simplify this expression, we need to expand the squared term:

V = π(16x^2 + 8x + 1)(3x+4)

Next, we can use the distributive property to multiply the two binomials:

V = π(48x^3 + 64x^2 + 24x + 12x^2 + 16x + 4)

Simplifying the terms inside the parentheses, we get:

V = π(48x^3 + 76x^2 + 40x + 4)

Finally, we can multiply the entire expression by π and write it in standard form:

V = 48πx^3 + 76πx^2 + 40πx + 4π

Therefore, the polynomial in standard form for the volume of the cylinder is 48πx^3 + 76πx^2 + 40πx + 4π.

yummie

Thanks answered