Geometry Surface Area Problem.

Question

Soda cans are made out of aluminum and are shaped like a cylinder. The formula for the surface area of a cylinder can be used to find the amount of aluminum, in square centimeters, that is needed to make a soda can.

 

A typical soda can measures 12 centimeters tall and has a volume of 235.5 cubic centimeters. To the nearest whole number, how many square centimeters are required to make a can?

 

A. 39 Square centimeters

B. 188 Square centimeters

C. 208 Square centimeters

D. 228 Square centimeters

 

An explanation of how you arrived at the answer you did would be much appreciated so I know how to do problems like this one in the future.

Answer 1

The volume of a cylinder is equal to pi*r²*h  (this is the area of the base, which is a circle, times the height).  You are given the height (12 cm) and the volume (235.5 cc) so you can solve for r, the radius of the cylinder  

 

V = 235.5 = pi*r²*12  

r² = 235.5/(12*pi) = 6.246832 

r = 2.499 cm ~ 2.5 cm 

 

The surface area of a cylinder is equal to 2*(pi*r²) + 2*pi*r*h.  The first term is the area of the top and bottom of the cylinder (they are both circles with radius r) and the second term is the area of the curved side of the cylinder (this is a circle with circumference 2*pi*r and height h).  So plug in r = 2.5 and h = 12 to this formula  

 

SA = 2*pi*2.5² + 2*pi*2.5*12

     = 12.5*pi + 60*pi

     = 72.5*pi

     = 227.8 square centimeters ~ 228