cylinder
Source: geocone1, thinkquest.org
Example: The formula S = π √r2 + h2 , reprsents the surface area of a cone where r is the radius of the base and h is the height. Find the approximate radius of a cone with a height of 8 inches and a surface area of 40 square inches?

Substitute the given information (S=40, h=8) into the formula.

 
S = π √r2  + h2
 
40 = S = π √r2  + 82
Simplify
(82=64) ⇒ 40 = π √r2  + 64
Divide both sides by π
To "undo" the square root, square both sides
 
Subtract 64 from both sides
Take the square root of both sides to "undo" the r2
Simplify to find r

Notice there is a (±) symbol in front of the square root.

Since you are solving for r2, when you take the square root of both sides, there are two solutions. But, since r is the length of the radius and length cannot be negative, you are only interested in the positive answer.

When you are solving you may use a calculator to simplify 40 π ≈ 12.73

Solution: The radius of the cone is Interactive button. Assistance may be required. _____________. ≈ 9.9 inches.

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