Question

The answer if any body knows it

Answer 1

`A=\pi(336)`

`A=1055.575`

Explanation:

1. Approach

One is given a prism. The base of the prism is a quarter of a circle, the prism's length is also given. The easiest method to find the volume of the prism is to find the area of the quarter of the circle, then multiply the result by the length of the prism.

2. Find the area of the quarter circle

The following formula can be used to find the area of a circle,

`A_c=(\pi)(r^2)`

Since one is trying to find the area of a quarter of a circle, one must multiply this formula by (
`(1)/(4)`). Please note that the parameter (r) represents the radius of the circle or the distance from the center of the circle to the circumference or outer edge of the circle. The parameter (
`\pi`) represents the number (
`3.1415...`).

`A_c=(1)/(4)(\pi)(r^2)`

Substitute the given values into the formula and simplify to evaluate,

`A_c=(1)/(4)(\pi)(r^2)`

`A_c=(1)/(4)(\pi)((8)^2)`

`A_c=(1)/(4)(\pi)(64)`

`A_c=(\pi)(16)`

`A_c\approx 50.2655`

3. Find the volume of the prism

Now multiply the area of the quarter circle by the length of the prism to find the volume of the prism. Note that the parameter (l) represents the length of the prism,

`A=A_c(l)`

Substitute and simplify to evaluate,

`A=(\pi)(16)(21)`

`A=\pi(336)`

`A=1055.575`