Find the length of an arc of a circle if the diameter is 24cm and the arc measur...

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nezuko89 @nezuko89

October 2022 1 7 Report

Find the length of an arc of a circle if the diameter is 24cm and the arc measures 90°?

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UK2019

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✏️ARC LENGTH

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Problem: Find the length of an arc of a circle if the diameter is 24 cm and the arc measures 90°?

Solution: Find the length of the arc in which it is the product of the ratio of the angle subtended to it at 360 degrees, and the circle's circumference.

$\begin{aligned}& \bold{ \color{lightblue}Formula: } \\ & \boxed{ \ell = \frac{ \theta}{360 \degree} \cdot2\pi r } \end{aligned}$

- The diameter of the circle is twice its radius, thus we can say that the circumference of the circle is the product of its diameter and pi.

$\begin{aligned}{ \ell = \frac{90 \degree}{360 \degree} \cdot2\pi(24cm) } \end{aligned}$

$\begin{aligned}{ \ell = \frac{1}{4} \cdot\pi(48cm) } \end{aligned}$

$\begin{aligned}{ \ell = \frac{\pi(48cm)}{4} } \end{aligned}$

$\begin{aligned}{ \ell = \pi(12cm)}\end{aligned}$

- Let 3.14 be the approximate value of pi.

$\begin{aligned}{ \ell≈ (3.14)(12cm)}\end{aligned}$

$\begin{aligned}{ \ell≈ 37.68cm}\end{aligned}$

- Therefore, the length of the arc is:

$\large \boxed{ \rm \green{ \: 37.68 \: cm \: }}$

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nezuko89 thank you po

UK2019 Naka answered na rin po yung isa (segment area)

UK2019 your welcome :)

nezuko89 pwede ung dalawa pa po hehe

nezuko89 ah isa nalang pala ate

eren57 @sanderangala hii! i've been seeing your answer rn and i've learned a lot, especially the formulas. Thankyouu!

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