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
ANSWERED
asked 2021-05-22
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.

Answers (1)

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.
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