Question

use terms from the list below to complete the sentences.
slant height \t\t\t circumference
cylinder \t\t\t pythagorean theorem

1. the volume of a cone is equal to one third of the volume of a

____________________ with the same radius and height.

1. the height, radius, and ____________________ of a cone

form a right triangle. if you know two of these dimensions, you
can use the ____________________ to find the third
dimension.

1. you can find the radius of a cone if you know the

____________________ of the base.

Explanation:

1. The volume formula of a cone \(V=\frac{1}{3}\pi r^{2}h\) and the volume formula of a cylinder \(V = \pi r^{2}h\). When they have the same radius \(r\) and height \(h\), the volume of the cone is one - third of the volume of the cylinder.
2. For a cone, if we consider the right - triangle formed by the height \(h\), radius \(r\), and slant height \(l\) (\(l=\sqrt{h^{2}+r^{2}}\) by the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\), where \(a = h\), \(b = r\), \(c = l\)).
3. The formula for the circumference of a circle (the base of the cone) is \(C = 2\pi r\), from which we can solve for \(r=\frac{C}{2\pi}\) if we know the circumference \(C\).

Answer:

1. cylinder
2. slant height; Pythagorean Theorem
3. circumference