Question

# Solve each problem. Show your work. The diameter of a circle is 12 inches. Find the area of a sector of the circle with a central angle that measures 110∘. Use 3.14 for π.π. Round to the nearest hundredth.

Math Word Problem
Solve each problem. Show your work. The diameter of a circle is 12 inches. Find the area of a sector of the circle with a central angle that measures 110∘. Use 3.14 for π.π. Round to the nearest hundredth.

2021-05-23
Determine the value of the radius.
$$\displaystyle{r}=\frac{{d}}{{2}}=\frac{{12}}{{2}}={6}$$
Determine the area of the sector.
$$\displaystyle{A}=\frac{{N}}{{360}}{\left(π{r}^{{2}}\right)}$$ Write the formula for area of a sector
$$\displaystyle{A}=\frac{{110}}{{360}}{\left({3.14}\right)}{\left({6}^{{2}}\right)}$$ Substitute the values
$$\displaystyle{A}=\frac{{11}}{{360}}{\left({3.14}\right)}{\left({36}\right)}$$ Evaluate the exponent
$$\displaystyle{A}=\frac{{11}}{{36}}{\left({3.14}\right)}{\left({36}\right)}$$ Simplify the fraction
A ~ 34.54 Multiply the values.