Question

GEOMETRY Use the formula$V=\mathbf{\pi }{r}^{2}h$ to find the volume of the cylinder.

Short answer

The volume of cylinder is $\mathbf{45}\mathbf{\pi }{x}^4$.

Step-by-step solution

Step 1. Replace the variables with their values.

Replace r with 3x and h with$5x^2$ into $V=\pi r^{2}h$.

$V=\pi {\left(3x\right)}^2\left(5x^2\right)$

Step 2. Group the coefficients and the variables.

Group the coefficients and variables in the given expression.

$V=\left(\pi \cdot 3^2\cdot 5\right)\left(x^2\cdot x^2\right)$

Step 3. Write the property of product of powers.

For any real number a and any integers m and n, $a^m\cdot a^n=a^{m+n}$.

Step 4. Apply property of product of powers and simplify.

Apply the property of product of powers to the expression obtained in step 2 and simplify.

$$\begin{gathered} V=\left(\pi \cdot 3^2\cdot 5\right)\left(x^{2+2}\right) \\ =45\pi x^4 \end{gathered}$$

Therefore, volume of cylinder is $45\pi x^4$.