Question

rectangle paperboard 32in long22 in widehas a semicircle cut out of itfind the area of the remaining paperboard using the value 3.14 for pie

Answer 1

To solve the exercise, we find the area of the rectangle. Then we subtract the area of the semicircle.

`\begin{gathered} A_R=A_r-A_s \\ \text{ Where} \\ A_R\text{ is the area of the remaining paperboard} \\ A_{r\text{ }}is\text{ the area of the rectangle} \\ A_s\text{ is the area of the semicircle} \end{gathered}`

The formula to find the area of a rectangle is:

`A_r=\text{ length}\cdot\text{ width}`

Then, we have:

`\begin{gathered} A_r=32in\cdot22in \\ A_r=704in^2 \end{gathered}`

The formula to find the area of a semicircle is:

`\begin{gathered} A_s=(\pi\cdot r^2)/(2) \\ \text{ Where r is the radius of the semicircle} \end{gathered}`

The radius is equal to half of the diameter. Then, we have:

`\begin{gathered} A_s=(\pi\cdot r^2)/(2) \\ A_s=(3.14\cdot(11in)^2)/(2) \\ A_s=(3.14\cdot121in^2)/(2) \\ A_s=(379.94in^2)/(2) \\ A_s=189.97in^2 \end{gathered}`

Finally, we subtract the areas:

`\begin{gathered} A_R=A_r-A_s \\ A_R=704in^2-189.97in^2 \\ A_R=514.03in^2 \end{gathered}`

Therefore, the area of the remaining paperboard is 514.03 square inches.