Question

A cylindrical can has a volume of and is tall. What is its diameter?

Short answer

The diameter of the cylinder is 4 cm.

Step-by-step solution

Step-1. Setup the model.

The volume of the cylinder is $\pi r^{2}h.$ where is the height and r is the radius.

Height of the cylinder is $10\mathrm{cm}.$

Volume of the cylinder$=40\pi {\mathrm{cm}}^3$

We need to find the diameter of the cylinder.

Step-2. Solve for radius.

$\begin{array}{l}V=\pi r^{2}h\\ 40\pi =\pi r^2\left(10\right)\\ 4=r^2\\ r=2\end{array}$

Radius of the cylinder is 2 cm.

Step-3. Solve for diameter.

Diameter is twice of the radius.

$d=2r$

Put 2 for r.

$\begin{array}{l}d=2\left(2\right)\\ d=4\end{array}$

Hence, the diameter of the cylinder is 4 cm.