Question

volume of cylinders, cones, and spheres pre - test complete 1 2 3 4 5 6 7 8 9 10 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: Recall the volume formula for a cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Given that the height $h$ is equal to the diameter of the base, and if the radius is $r$, the diameter $d = 2r$, so $h = 2r$. The volume $V = 18\pi$.

Step2: Substitute values into the formula

Substitute $h = 2r$ and $V=18\pi$ into $V=\frac{1}{3}\pi r^{2}h$. We get $18\pi=\frac{1}{3}\pi r^{2}(2r)$.

Step3: Simplify the equation

First, cancel out $\pi$ on both sides of the equation. We have $18=\frac{1}{3}(2r^{3})$. Then multiply both sides by 3 to get $54 = 2r^{3}$. Divide both sides by 2, we obtain $r^{3}=27$.

Step4: Solve for $r$

Take the cube - root of both sides. Since $\sqrt[3]{r^{3}}=r$ and $\sqrt[3]{27}=3$, we find that $r = 3$.

Answer:

3 units