The volume of a cylinder is given by the formula cap v is equal to pi r squared h , where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius open paren x plus 8 close paren and height open paren 2 x plus 3 close paren Which expression represents the volume of the can?
Answer
A
2 pi x cubed plus 35 pi x squared plus 80 pi x plus 48 pi
B
pi x cubed plus 19 pi x squared plus 112 pi x plus 192 pi
C
2 pi x cubed plus 35 pi x squared plus 176 pi x plus 192 pi
D
4 pi x cubed plus 44 pi x squared plus 105 pi x plus 72 pi
Explanation
Use the cylinder volume formula V = πr²h. Substituting r = x + 8 and h = 2x + 3 gives V = π(x + 8)²(2x + 3). First, (x + 8)² = x² + 16x + 64; multiplying by (2x + 3) gives 2x³ + 35x² + 176x + 192. Therefore, the volume is 2πx³ + 35πx² + 176πx + 192π, choice C.
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