Find the Volume of the Cone

Question

Find the volume of a cone with a base radius of 5yd

 and a height of 7yd.

Write the exact volume in terms of π, and be sure to include the correct unit in your answer.

Answer 1

A cone is a shape with a circle at the bottom and a point at the top. So its volume formula is similar to the area of a circle (πr²) and the volume of a cylinder (πr²h). In these formulas, r means radius and h means height. Because a cone is like a cylinder but thinner at the top, you start with a cylinder volume and reduce it. The neat way geometry works, it's actually always 1/3 of the cylinder in volume.

V_cone = πr²h * 1/3

Plug in the values...

π(5)²(7) * 1/3

π(25)(7) * 1/3

(25)(7)(1/3)π

(175/3)π

175π/3

For the units, remember that they were both yards, so let's just plug in "yd" to see what happens to it...

π(yd)²(yd) * 1/3

π(yd)²(yd)¹ * 1/3

π(yd)³ * 1/3

(Note we are ignoring everything but the "yd" and its exponents!)

We get cubic yards. And that makes sense, because we're finding a volume (power 3), not a length (power 1) or area (power 2).

Final answer: 175π/3 yd³ (aka cubic yards).