Question

two identical cones are inscribed in a cylinder. which equation represents the volume of each cone? a. v = \frac{\pi r^{2}h}{6} b. v = \frac{\pi r^{2}h}{2} c. v = \frac{\pi r^{2}h}{3} d. v = \frac{\pi r^{2}h}{4}

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \( V=\frac{1}{3}\pi r^{2}h \).

Step2: Determine the height of each cone

Since two identical cones are inscribed in a cylinder of height \( H \), the height of each cone \( h = \frac{H}{2} \).

Step3: Substitute the height into the cone - volume formula

Substitute \( h=\frac{H}{2} \) into \( V = \frac{1}{3}\pi r^{2}h \). We get \( V=\frac{1}{3}\pi r^{2}\times\frac{H}{2}=\frac{\pi r^{2}H}{6} \).

Answer:

A. \( V=\frac{\pi r^{2}H}{6} \)