Question

1. a circle has radius 10 m. find the length of an arc intercepted by a central angle of 72°.

leave answer in terms of π

1. in a circle with radius 15 cm, a central angle of 120° intercepts an arc. find the arc length.

round to nearest tenth

Explanation:

Question 4

Step1: Recall arc length formula

The formula for the length of an arc \( s \) is \( s=\frac{\theta}{360^\circ}\times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Substitute values

Given \( r = 10\space m \) and \( \theta=72^\circ \). Substitute into the formula:
\( s=\frac{72^\circ}{360^\circ}\times 2\pi\times 10 \)

Step3: Simplify the expression

First, simplify \( \frac{72^\circ}{360^\circ}=\frac{1}{5} \). Then:
\( s=\frac{1}{5}\times 20\pi = 4\pi \)

Step1: Recall arc length formula

The formula for the length of an arc \( s \) is \( s=\frac{\theta}{360^\circ}\times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Substitute values

Given \( r = 15\space cm \) and \( \theta = 120^\circ \). Substitute into the formula:
\( s=\frac{120^\circ}{360^\circ}\times 2\pi\times 15 \)

Step3: Simplify the expression

Simplify \( \frac{120^\circ}{360^\circ}=\frac{1}{3} \). Then:
\( s=\frac{1}{3}\times 30\pi= 10\pi \)
Now, calculate the numerical value: \( 10\pi\approx 10\times 3.1416 = 31.416 \)

Step4: Round to nearest tenth

Rounding \( 31.416 \) to the nearest tenth gives \( 31.4 \)

Answer:

\( 4\pi \) meters

Question 5