Question

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

A)
`\pi`
`x^(3)`+19
`\pi`
`x^(2)`+112
`\pi`x+192
B) 2
`\pi`
`x^(3)`+35
`\pi`
`x^(2)`+80
`\pi`x+48
`\pi`
C) 2
`\pi`
`x^(3)`+35
`\pi`
`x^(2)`+176
`\pi`x+192
`\pi`
B) 4
`\pi`
`x^(3)`+44
`\pi`
`x^(2)`+105
`\pi`x+72
`\pi`

Answer 1

The answer is D
3pix^3+20pix^2+44pix+32pi

Answer 2

Volume of cylinder =
`\pi r^(2)h`

Substituting
`r=x+8` and height =
`2x+3`

Volume =
`\pi (x+8)^(2) (2x+3)`, expanding the
`(x+8)^(2)`
Volume =
`\pi ( x^(2) +16x+64)(2x+3)`, expanding the last two brackets
Volume =
`\pi ( 2x^(3)+3 x^(2) +32 x^(2) +48x+128x+192)`, then simplify
Volume =
`\pi ( 2x^(3) +35 x^(2) +176x+192)`, then mulitply out pi
Volume =
`2 \pi x^(3)+35 \pi x^(2) +176 \pi x+192 \pi`