Question

The area of this circle is 42π m².

Answer 1

We will solve this question using the formula for the area of a sector of a circle. We know that the area, A, of a sector of a circle is given by:

$A=\frac{\theta}{360^{\circ}}\times \pi r^2$

Where $\theta$ is the angle subtended by the sector at the center of the circle. Also, we know that in our case, $\theta=60^{\circ}$.

Now, we know that $\pi r^2$ is just the area of the original circle in question here, which has been given to us a $42 \pi$.

Thus, the required area of the sector in question here is:

$A=\frac{60^{\circ}}{360^{\circ}}\times 42\pi =\frac{1}{6}\times 42 \pi =7 \pi$

Thus the area of a 60º sector of this circle is $7 \pi$ m^2.

Thus, the second option is the correct option.

Answer 2

A full circle is 360°, so a 60° circle is 1/6th of the area.

1/6th of 42π m² is 7π m², so answer B.