Question

The radius of a cylindrical box is (2x+3) inches. Height of the gift box is 3 times the radius. What is the surface area of cylinder? write answer as a polynomial in standard form.

Answer 1

The surface area of cylinder in standard form is:

$A = 100.48x^2+301.44x + 226.08$

Solution:

Given that,

Radius of cylinder = 2x + 3 inches

Height of cylinder = 3 times radius = 3(2x + 3)

Height of cylinder = 6x + 9 inches

The surface area of cylinder is given by formula:

$A=2 \pi rh+2 \pi r^2\\\\A = 2 \pi r(h+r)$

Where, "r" is the radius and "h" is the height of cylinder

Substituting the given values we get,

$A = (2 \times 3.14 \times (2x+3))(6x + 9 + 2x + 3)\\\\A = (6.28 \times (2x+3))(8x + 12)\\\\A = (12.56x + 18.84)(8x+12)\\\\On\ simplifying\ we\ get\\\\\ A = 100.48x^2 +150.72x+150.72x + 226.08\\\\A = 100.48x^2 + 301.44x+226.08$

Thus the surface area of cylinder in standard form is found