PLEASE HELP MMMMMEEEEEEThe cylinder shown has a lateral surface area of about 750 square inches. Which answer is closest to the measure of the cylinder's radius? Use 3.14 to approximate pi. the height being 50 inches.a) 2.19 inchesb) 2.39 inchesc.) 15 inchesd) 75 inchesplease walk me through how to solve this, though if you don't have time to explain it then it's okay too..
Accepted Solution
A:
Imagine taking a soup can and peeling off the label. This label fully covers the curve side. What comes off is a flat piece of paper. If no tears are made, you'll have a rectangle after its fully peeled off.
The rectangle will have a width of W = 50 (same as the height of the can) and a length of L = 2*pi*r (same as the circumference of the base). So the area of this rectangle is A = W*L = 50*2*pi*r = 100*pi*r
The expression 100*pi*r represents the lateral surface area for this particular cylinder
We are given that the lateral surface area is 750 square inches, so this is the area of the label that peels off meaning A = 750
Equate the two values and solve for r 100*pi*r = 750 pi*r =750/100 pi*r = 7.5 r = 7.5/pi r = 7.5/3.14 r = 2.3885 which rounds to 2.39