Question

what is the volume of the cone? use π ≈ 3.14
12.56 cubic units
18.84 cubic units
20.93 cubic units
25.12 cubic units

Explanation:

Step1: Identify radius and height

The radius $r$ of the cone is 2 (half of the diameter 4), and we need to find the height $h$. Using the Pythagorean theorem for the cone's slant - height $l = 5$, $h=\sqrt{l^{2}-r^{2}}=\sqrt{5^{2}-2^{2}}=\sqrt{25 - 4}=\sqrt{21}\approx4.58$. But if we assume the 5 is the height and 4 is the diameter (radius $r = 2$), we use the volume formula directly.

Step2: Apply volume formula

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 2$, $h = 5$ and $\pi=3.14$ into the formula: $V=\frac{1}{3}\times3.14\times2^{2}\times5=\frac{1}{3}\times3.14\times4\times5=\frac{62.8}{3}\approx20.93$.

Answer:

20.93 cubic units