The radius of a cylindrical gift box is (2x+3) in. The height of the gift box is three times the radius. What is the surface area of the cylinder? Write your answer as a polynomial form.

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asked Feb 23, 2020 139k views

3 votes

The radius of a cylindrical gift box is (2x+3) in. The height of the gift box is three times the radius. What is the surface area of the cylinder? Write your answer as a polynomial form.

Mathematics
college

Cipous asked

by Cipous

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1 Answer

3 votes

Answer:

75.36x^3+339.12x^2+508.68x+254.34

Explanation:

The volume of the cylinder with radius (2x+3) and height 3(2x+3) = 6x+9 is

$V=\pi ((2x+3)^2)(6x+9)\\ V=\pi (4x^2+12x+9)(6x+9)\\ V=(24x^3+72x^2+54x+36x^2+108x+81)\pi \\ V=3.14(24x^3+108x^2+162x+81) \\ V=75.36x^3+339.12x^2+508.68x+254.34$