Geometry word problem please help ASAP

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

Picture a rectangular piece of paper 12 inches tall and rolled into a cylinder, the surface area is the height times the circumference of the circle - which is the length of the paper.

 

You'll have to work backwards from the given volume of the cylinder, to find the radius, so you can find the circumference.

 

The volume of the can is the area of the bottom times the height, the area of the bottom is a circle and the area of a circle A = (pi)(r²). 

 

Part A: To find the radius of the can:

divide 235.5 cm³ by 12 to get the area of the bottom,

 

divide that number by pi to get the square of the radius

 

take the square root of that to find the radius (I got about 2.5)

 

 

Part B: Find the circumference of the can:

multiply the radius by (2)(pi) to find the circumference of the can

 

Part C: Find the lateral surface area (the area of the side of the can):

Multiply the circumference of the can by 12 to get the lateral surface area of the can

 

Do you need to include the area of the top and the bottom to get the total amount of aluminum to make the can?

 

One of the choices above includes the area of the top and the bottom along with the lateral surface area, one of the answers has the lateral surface area only.