Geometry - Right circular cone - volume/area

http://tinypic.com/r/wri8nr/6

1.) If r = 12 in, and h = 16 in, find the slant height.
a. 4 in.
b. 20 in.
c. square root of 112 in.
d. 19 in.

2.) If r = 4 in, and h = 3 in, find the total surface area.
a. 24π square in.
b. 12π square in.
c. 36π square in.
d. 72π square in.

3.) If volume = 24π cubic cm and r = 3, find the height.
a. 6 cm
b. 8 cm
c. 12 cm
d. 16 cm

Thanks so much to anyone who gives me the correct answers!! Please try to explain if you can. I will pick a best answer!

1. The slant height is the easiest to find. If you look at a cone from the side, the radius (r), height (h), and side (s) form a right triangle. You're given the radius (r = 12) and the height (h = 16). Simply plug these into the Pythagorean equation to solve for the unknown:

r² + h² = s²

12² + 16² = s²

144 + 256 = s²

400 = s²

20 = s

The slant height is 20 in (Answer B)


2. Looking at my handy-dandy About.com website (http://math.about.com/od/formulas/ss/sur… I obtain the formula for total surface area of a cone as:

SA = πrs + πr²

First find s (see #1, above)

s = √(r² + h²) = √(16 + 9) = √25 = 5

Plug the numbers into the formula and solve:

SA = πrs + πr²

SA = (4)(5)π + (4²)π in² = (20 + 16)π in² = 36π in² (Answer C)


3. The formula for the volume of a cone is:

V = (1/3)πr²h

So the formula for the height of a cone is:

(1/3)πr²h = V
πr²h = 3V
h = 3V/πr²

Plug in the numbers:

h = 3(24π)/π(3²) = 3(24)/9 = 24/3 = 8 cm (Answer B)

1.) Try to picture that the "side" of the cone at a front view is like a right triangle. The slant height is the hypotenuse, the radius is the side on the bottom, and the height is the other side. You can use pythagorean theorem to find the slant height. The formula is a squared + b squared = c squared. C is always the hypotenuse. So 12 squared plus 16 sqaured = the square root of c. Therefore, 144+256 = the square root of c. Simplified, 400 = the square root of c. The square root of 400 is 20, so the slant height is 20 in.