Question

The diagram shows a sector of a circle of radius r cm containing angle Ө radians. The area of the sector is Acm2 and the perimeter of the sector is 50 cm.
a. Find Ө in terms of r.
b. Show that A = 25r – r2

Answer 1

Answer on Question #70689 – Math – Trigonometry

Question

The diagram shows a sector of a circle of radius $r$ cm containing angle $\Theta$ radians. The area of the sector is $Acm^2$ and the perimeter of the sector is $50$ cm.

a. Find $\Theta$ in terms of $r$.

b. Show that $A = 25r - r^2$

Solution

a.

$$S = \frac{\alpha \cdot R^2}{2}$$ $$A = \frac{\theta \cdot r^2}{2}$$ $$\theta = \frac{2A}{r^2}$$

b.

$$P = \alpha \cdot r + 2r$$ $$50 = \theta \cdot r + 2r$$ $$50 = \frac{2A}{r^2} \cdot r + 2r$$ $$25 = \frac{A}{r} + r$$ $$A = 25r - r^2$$

Answer:

a. $\theta = \frac{2A}{r^2}$

b. $A = 25r - r^2$

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