The answer is 54πx² + 144πx + 96π
The surface area of cylinder (SA) is:
SA = 2 π r h + 2 π r²
<span>The height of the gift box is twice the radius: h = 2r
r = 3x + 4
h = 2(3x + 4) = 6x + 8
SA = </span>2 π r h + 2 π r²
SA = 2π (r * h + r²)
SA = 2π ((3x + 4)(6x + 8) + (3x + 4)²)
SA = 2π(18x² + 24x + 24x + 32 + 9x² + 24x + 16)
SA = 2π(27x² + 72x + 48)
SA = 54πx² + 144πx + 96π
To solve this, it might be easier to draw it out (see the picture below). I split it into two triangles and used trig functions to find the altitude. I used the big triangle to find theta, and the used theta to find the side of the altitude. *remember that sine= opposite/hypotenuse*
Because it is a question asking for ppl playing either soccer OR basketball, we add the two fractions together. Thus, Part A becomes 3/10 + 4/10, which is 7/10 (since the denominators are the same, you only add the numerators).
