Question

a rectangular cardboard that measures 20 in in length and 15 in in width has had a semi - circle cut out. what is the remaining area after cutting the semi - circle? (use the value 3.14 for π, and do not round the answer.)

Explanation:

Step1: Calculate rectangle area

The area formula for a rectangle is $A = l\times w$. Here, $l = 20$ in and $w = 15$ in, so $A_{rectangle}=20\times15 = 300$ square - inches.

Step2: Calculate semi - circle area

The diameter of the semi - circle is 15 in, so the radius $r=\frac{15}{2}$ in. The area formula for a full - circle is $A=\pi r^{2}$, and for a semi - circle is $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substituting $r = \frac{15}{2}$ in and $\pi = 3.14$, we get $A_{semicircle}=\frac{1}{2}\times3.14\times(\frac{15}{2})^{2}=\frac{1}{2}\times3.14\times\frac{225}{4}= \frac{3.14\times225}{8}=88.3125$ square - inches.

Step3: Calculate remaining area

The remaining area $A_{remaining}=A_{rectangle}-A_{semicircle}$. Substituting the values of $A_{rectangle}$ and $A_{semicircle}$, we have $A_{remaining}=300 - 88.3125=211.6875$ square - inches.

Answer:

$211.6875$ square inches