Question

The radius of a cylinder gift box is box is 3X +1 inches the height of the gift box is twice the radius what is the surface area of the cylinder write your answer as a polynomial in standard form

Answer 1

Answer:

The surface area of the gift box is = $A = \frac{1188}{7}x^{2}+ \frac{774}{7}x +\frac{132}{7}$

Step-by-step explanation:

The surface area of the cylinder can be calculated using this formula:

$A=2\pi rh+2\pi r^2$

in this case, r is not a number, but rather an expression, which is r = $3x +1$.

The height of the gift box is twice the radius, which is h = $2(3x+1)= 6x+2$

To get our curved surface area, we carefully put the expressions for h and r into the equation.

$A = 2 \times \frac{22}{7} \times (3x+1) \times (6x+2) + 2 \times \frac{22}{7} \times (3x+1)^{2}$

$A = \frac{44}{7} (3x+1) \times (6x +2) + \frac{44}{7} (9x^{2} + 6x +1)\\A =\frac{132}{7}x + \frac{44}{7} \times (6x+2)+ \frac{396}{7}x^{2}+\frac{246}{7}x +\frac{44}{7}$

$A = \frac{792}{7}x^{2} +\frac{264}{7}x +\frac{264}{7}x + \frac{88}{7} + \frac{396}{7}x^{2} + \frac{246}{7}x + \frac{44}{7}$

$A = \frac{1188}{7}x^{2}+ \frac{774}{7}x +\frac{132}{7}$

The surface area of the gift box is = $A = \frac{1188}{7}x^{2}+ \frac{774}{7}x +\frac{132}{7}$