Question

an oblique cone has a height equal to the diameter of the base. the volume of the cone is equal to 18π cubic units. what is the radius of the cone? 2 units 3 units 6 units 9 units

Explanation:

Step1: Define variables

Let radius $r = x$, height $h = 2x$ (since diameter is $2x$, height equals diameter).

Step2: Volume formula for cone

Volume $V = \frac{1}{3}\pi r^2 h$. Substitute $r=x$, $h=2x$, $V=18\pi$:
$$18\pi = \frac{1}{3}\pi x^2 (2x)$$

Step3: Simplify and solve for $x$

Cancel $\pi$ from both sides:
$$18 = \frac{2}{3}x^3$$
Multiply both sides by $\frac{3}{2}$:
$$x^3 = 18 \times \frac{3}{2} = 27$$
Take cube root:
$$x = \sqrt[3]{27} = 3$$

Answer:

3 units