Question

What is the perimeter of a quadrant whose radius is 14cm​

Answer 1

(28 + 7π) cm ≈ 50.0 cm (nearest tenth)

Explanation:

A quadrant is a quarter section of a whole circle.

The perimeter of a quadrant is made up of two radii and the intercepted arc length.

The formula for an arc length is rθ, where r is the radius, and θ is the central angle measured in radians.

The central angle of a quadrant π/2 radians.

Therefore, the formula for the perimeter of a quadrant of a circle is:

`\boxed{P_(\sf quadrant)=2r+(\pi)/(2)r}`

Given the radius of the quadrant is 14 cm, substitute r = 14 into the formula:

`\begin{aligned}\sf Perimeter&=2(14)+(\pi)/(2)(14)\\\\&=28+7\pi\\\\&=28+21.9911485...\\\\&=49.9911485...\\\\& \approx 50.0\; \sf cm\; (nearest\;tenth)\end{aligned}`

Therefore, the perimeter of a quadrant whose radius is 14 cm is exactly (28 + 7π) cm or approximately 50.0 cm, rounded to the nearest tenth.