Q29. - Algebra 1

Question

GEOMETRY The volume of a cylinder is $\mathrm{\pi }$ times the radius $r$ squared multiplied by the height $h$. Write an expression for the volume.

Step-by-Step Solution

Answer

The expression for the volume of a cylinder is $\pi r^{2}h$.

Step 1. Apply the concept of algebraic expression.

An algebraic expression is a combination of constants, variables, and arithmetic operations.

Step 2. Write given information.

Given: The volume of a cylinder is $\mathrm{\pi }$ times the radius $r$ squared multiplied by the height $h$.

Step 3. Write the verbal expression into an algebraic expression.

Here, “$\mathrm{\pi }$ times the radius $r$ squared” denotes $\mathrm{\pi }$ multiplied by $r^2$ i.e.  $\pi r^{\mathit{2}}$

Also, “$\mathrm{\pi }$ times the radius $r$ squared multiplied by the height $h$” denotes  $\pi r^{\mathit{2}}$ multiplied by $h$ that is $\pi r^{2}h$.

Thus, the expression for the volume of a cylinder is $\pi r^{\mathit{2}}h$.