The Surface Area (SA) of a can is given by the formula SA=2pR^2+2prh, where R is the radius of the circular top of the can and h is the height of the can.

Question

If a can has a surface of 1032 square inches and a height of 7.55 inches, what is the radius of the circular top? Round to the nearest hundredth. 

Answer 1

Area of a circle is π*R², where R is the radius.

Lateral Surface Area is 2*π*R*h, where R is the radius and h is the height.

 

From your equation above, SA = 2*π*R2+2*π*R*h, there is a top and bottom to a can, hence the first term 2*π*R2.

 

Therefor pluging in the known values:

SA = 1032in2

h   =  7.55in

 

1032in^{2 =} 2*π*R²+2*π*R*7.55(in)

 

1032in² = (2*π)*(R²+R*7.55(in))

 

1032in²/(2*π)=R²+7.55in*R

 

0=R²+7.55in*R-1032in²/(2*π)

 

use the quadratic formula:

x = [ -b ± √(b^2 - 4ac) ] / 2a

 

plugging in your values will give you two answers -17.14in or 9.59in, in this case your answer is the positive lenght.