OAB is a minor sector of a circle with area 48 m^2. Calculate the area of OAB, giving your answer to one decimal place.
Understand the Problem
The question requires us to calculate the area of a sector (OAB) of a circle, given that the area of the entire circle is 48 square meters and the central angle of the sector is 60 degrees. We need to provide the answer to one decimal place.
Answer
$8.0 \ m^2$
Answer for screen readers
$8.0 \ m^2$
Steps to Solve
- Calculate the fraction of the circle represented by the sector.
The sector has a central angle of $60^\circ$, and a full circle has $360^\circ$. Therefore, the sector represents $\frac{60}{360}$ of the circle.
- Simplify the fraction.
$\frac{60}{360}$ simplifies to $\frac{1}{6}$.
- Calculate the area of the sector.
The area of the circle is $48 \ m^2$. The area of the sector is $\frac{1}{6}$ of the area of the circle. So, we multiply the area of the circle by $\frac{1}{6}$:
Area of sector = $\frac{1}{6} \times 48 \ m^2 = 8 \ m^2$
$8.0 \ m^2$
More Information
The area of the sector is exactly $8 \ m^2$. Since the question asks for the answer to one decimal place, we should write it as $8.0 \ m^2$.
Tips
A common mistake is to not simplify the fraction $\frac{60}{360}$ before calculating the area of the sector, but it does not affect the answer, as long as the calculations are done correctly. Another common mistake is to not round the answer to 1 decimal place or not include the units in the answer.
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