Question

The volume of a cylinder is expression represents the volume of the can?given by the formula v=pie r^2h, 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 ) pie x^3+19 pie x^2+112 pie x +192 pie
b) 2 pie x^3 +35 pie x^2+80 pie x + 48 pie
c) 2 pie x^3 + 35 pie x^2 +176 pie x + 192 pie
d) 4 pie x^3 + 44 pie x^2 + 105 pie x + 72pie

Answer 1

input
V=pi(x+8)^2(2x+3)
V=pi(x^2+16x+64)(2x+3)
V+pi(2x^3=35x^2+176x+192)
V=2πx³+35πx²+176πx+192π

Answer 2

For this case we have the following expression:

`v = pir ^ 2h`
Substituting values we have:

`v = pi (x + 8) ^ 2 (2x + 3)`
Rewriting we have:

`v = pi (x ^ 2 + 16x + 64) (2x + 3) v = pi ((2x ^ 3 + 32x ^ 2 + 128x) + (3x ^ 2 + 48x + 192))`

`v = pi (2x ^ 3 + 35x ^ 2 + 176x + 192) v = (2pix ^ 3 + 35pix ^ 2 + 176pix + 192pi)`
Answer:
An expression that represents the volume of the can is:
c) 2 pie x^3 + 35 pie x^2 +176 pie x + 192 pie