Question

use the formula ( v = pi r^2 h ), where ( r ) is the radius and ( h ) is the height, to find the volume of the inside of this cylindrical pipe. the inside diameter is ( 8xy^2 ) and the height (length) of the pipe is ( 12xy^2 ).

Explanation:

Step1: Find the inner radius

The inside diameter is $8x^2y^2$, so radius $r = \frac{8x^2y^2}{2} = 4x^2y^2$

Step2: Identify the height

The height (length) of the pipe $h = 12x^2y^2$

Step3: Substitute into volume formula

Substitute $r$ and $h$ into $V=\pi r^2 h$:

$$\begin{align*} V&=\pi (4x^2y^2)^2 (12x^2y^2)\\ &=\pi (16x^4y^4)(12x^2y^2) \end{align*}$$

Step4: Multiply the coefficients and variables

$$ V=\pi \times 16 \times 12 \times x^{4+2}y^{4+2} = 192\pi x^6y^6 $$

Answer:

$192\pi x^6y^6$