An ice cream cone is 8 inches tall and

Question

An ice cream cone is 8 inches tall with a slant height of 10 inches . The opening of the cone is a circle.What is the diameter of the opening of the cone?

Answer 1

Hint: draw a diagram and apply Pythagoras' Theorem - $\sqrt{10^2-8^2}= ....$ This gives you half the diameter of the cone. By the way, if $r$ is the radius of the ice cream then you can see that $6:r=8:10$, whence the radius of your ice cream is 7.5 inch.

Answer 2

Imagine dropping a line directly down the center of the cone. The line will be 8 inches (the height of the cone). You can then draw a radius from the line out to the edge of the cone. You've created a right triangle. One side is 8, the hypotenuse is 10 (the "slant height") and the third side is the radius. Apply Pythagorean theorem ($r = \sqrt {10^2-8^2}$) or recognize that it's a Pythagorean triplet and you'll have the radius. Diameter is a pretty easy next step from there.

(Wouldn't normally repeat what Nicky Hekster said in his comment, but the ratios he set up are not correct, I don't think. The square root formula is.)

That is going to hold a lot of ice cream!