Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-A pendulum swings through an angle of 16° each second. If the pendulum is 12 cm in length and 62) the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing?
Round to the nearest hundredth.
A) $3.35 \mathrm {~cm} ^ { 2 }$
B) $40.21 \mathrm {~cm} ^ { 2 }$
C) $80.42 \mathrm {~cm} ^ { 2 }$
D) $20.11 \mathrm {~cm} ^ { 2 }$

Question

Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-A pendulum swings through an angle of 16° each second. If the pendulum is 12 cm in length and 62) the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing?
Round to the nearest hundredth. 
A) $3.35 \mathrm {~cm} ^ { 2 }$
B) $40.21 \mathrm {~cm} ^ { 2 }$
C) $80.42 \mathrm {~cm} ^ { 2 }$
D) $20.11 \mathrm {~cm} ^ { 2 }$

Quizplus · Accepted Answer

The area of a sector of a circle is given by the formula $A = \frac{1}{2} r^2 \theta$, where $r$ is the radius and $\theta$ is the central angle in radians. For a complete swing, the pendulum covers an angle of $16^\circ \times 2 = 32^\circ$ (since it swings through an angle of 16° each second and the complete swing lasts 2 seconds). To find the area covered by each complete swing, we need to convert the angle to radians ($32^\circ = \frac{32\pi}{180}$ radians) and use the given radius $r = 12$ cm. Plugging these values into the formula gives $A = \frac{1}{2} \times 12^2 \times \frac{32\pi}{180} \approx 40.21 \mathrm{cm}^2$, rounding to the nearest hundredth.

Find the Area of a Sector of a Circle Having θ\thetaθ

Find the Area of a Sector of a Circle Having $\theta$