Question

The volume of a cylinder is given by the formula V=πr²h, where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has the radius (x+8) and height (2x+3). Which expression represents the volume of the can?

A: πx³+19πr²+112πx+192π
B: 2πx³+35πx²+80πx+48π
C: 2πx³+ 35πx²+176πx+192π
D: 4πx³+ 44πx²+105πx+72π

Answer 1

C

Explanation:

V=πr²h

V=π(x^2+64)h

V=π(x^2+64)(2x+3)

V=π(2x^3+3x^2+128x+192)

C: 2πx³+ 35πx²+176πx+192π

Answer 2

C

Explanation:

We know that the volume of a cylinder is given by the formula:

`V=\pi r^2h`

And we want to find the expression that represents the volume when the radius is (x+8) and the height is (2x+3).

So, let's substitute (x+8) for r and (2x+3) for h. This yields:

`V=\pi (x+8)^2(2x+3)`

Let's expand.

Expand the square term first. We can use the perfect square trinomial pattern, which is:

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

Here, our a is x and b is 8. So:

`V=\pi (x^2+2(x)(8)+(8)^2)(2x+3)`

Simplify:

`V=\pi (x^2+16x+64)(2x+3)`

Expand further. This time, we will use the distribute property. So:

`V=\pi ((x^2+16x+64)(2x)+(x^2+16x+64)(3))`

Multiply:

`V=\pi((2x^3+32x^2+128x)+(3x^2+48x+192))`

Combine like terms:

`V=\pi((2x^3)+(32x^2+3x^2)+(128x+48x)+(192))`

Add:

`V=\pi(2x^3+35x^2+176x+192)`

Distribute the π:

`V=2\pi x^3+35\pi x^2+176\pi x+192\pi`

So, our answer is C.

And we're done!