Question

The plastic cylinder has a diameter of 2 cm. There is a rectangular 0.6 cm square prism through the middle of the cylinder, extending from the top to the bottom. The height of the cylinder is 6 cm. Find the volume of the cylinder without the prism.

Answer 1

Answer:

The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.

Step-by-step explanation:

The volume of the cylinder without the prism can be defined as the volume of the entire cylinder ($V_{cy}$), measured in cubic centimeters, minus the volume of the prism ($V_{pr}$), measured in cubic centimeters. That is:

$V = V_{cy}-V_{pr }$ (1)

$V = \frac{\pi}{4}\cdot D^{2}\cdot h - l^{2}\cdot h$

$V = \left(\frac{\pi}{4}\cdot D^{2}-l^{2} \right)\cdot h$ (2)

Where:

$D$ - Diameter of the cylinder, measured in centimeters.

$l$ - Side of the square prism, measured in centimeters.

$h$ - Height of the square prism, measured in centimeters.

If we know that $D = 2\,cm$, $l = 0.6\,cm$ and $h = 6\,cm$, then the volume of the cylinder without the prism is:

$V = \left[\frac{\pi}{4}\cdot (2\,cm)^{2}-(0.6\,cm)^{2} \right]\cdot (6\,cm)$

$V \approx 16.690\,cm^{3}$

The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.