Question

In circle L with m, angle, K, L, M, equals, 70, degreesm∠KLM=70 ∘ and K, L, equals, 5KL=5, find the area of sector KLM. Round to the nearest hundredth.

Answer 1

To find the area of sector \( KLM \) in circle \( L \), we will use the formula for the area of a sector, which is given by:

\[
\text{Area of sector} = \frac{\theta}{360} \times \pi r^2
\]

where:
- \( \theta \) is the central angle in degrees,
- \( r \) is the radius of the circle.

From the problem, we have:
- \( \theta = m\angle KLM = 70^\circ \)
- The length \( KL = 5 \), which implies that the radius \( r = 5 \).

Now, we can calculate the area of the sector \( KLM \):

\[
\text{Area of sector} = \frac{70}{360} \times \pi \times (5)^2
\]

Calculating \( (5)^2 \):

\[
(5)^2 = 25
\]

Now substitute this value into the area formula:

\[
\text{Area of sector} = \frac{70}{360} \times \pi \times 25
\]

Simplifying \( \frac{70}{360} \):

\[
\frac{70}{360} = \frac{7}{36}
\]

So, now we have:

\[
\text{Area of sector} = \frac{7}{36} \times \pi \times 25
\]

This simplifies to:

\[
\text{Area of sector} = \frac{175}{36} \pi
\]

To find a numerical value, we use \( \pi \approx 3.14 \):

\[
\text{Area of sector} \approx \frac{175}{36} \times 3.14
\]

Calculating \( \frac{175}{36} \):

\[
\frac{175}{36} \approx 4.8611
\]

Now, multiply this by \( 3.14 \):

\[
\text{Area of sector} \approx 4.8611 \times 3.14 \approx 15.249
\]

Rounding to the nearest hundredth, we obtain:

\[
\text{Area of sector} \approx 15.25
\]

Thus, the area of sector \( KLM \) is approximately \( \boxed{15.25} \).