Question

1. draw a cylinder with a diameter of 6 centimeters and a volume of 36π cubic centimeters.
2. determine the radius and the height of the cylinder from problem 1. show or explain your thinking. then label your drawing with the cylinder’s radius and height.

Explanation:

Step1: Find radius from diameter

The diameter is 6 cm, so radius $r = \frac{6}{2} = 3$ cm.

Step2: Use volume formula to solve for height

Volume formula for cylinder: $V = \pi r^2 h$. Substitute $V=36\pi$, $r=3$:
$$36\pi = \pi (3)^2 h$$
Simplify: $36\pi = 9\pi h$. Divide both sides by $9\pi$:
$$h = \frac{36\pi}{9\pi} = 4$$

Step3: Describe the cylinder drawing

Draw a 3D cylinder, label the radius (3 cm) on the circular base, and label the height (4 cm) on the vertical edge.

Answer:

• The cylinder has a radius of 3 cm and height of 4 cm.
• For the drawing: Sketch a cylinder, mark the radius of the circular base as 3 cm, and the vertical height as 4 cm.