Question

question 20 of 44
which of the following can be used to find the area of a circle?
a. ( dpi^2 )
b. ( pi r^3 )
c. ( pi d^2 )
d. ( rpi^2 )

Explanation:

Step1: Recall the formula for the area of a circle.

The area of a circle is given by the formula \( A=\pi r^{2} \), where \( r \) is the radius of the circle. Also, we know that the diameter \( d = 2r\), so \( r=\frac{d}{2}\). Substituting \( r=\frac{d}{2} \) into the area formula, we get \( A=\pi(\frac{d}{2})^{2}=\frac{\pi d^{2}}{4}\), which is not the same as option C (\(\pi d^{2}\)). Option A (\(d\pi^{2}\)) and option D (\(r\pi^{2}\)) are incorrect because they do not match the standard area formula of a circle. Option B is \( \pi r^{2} \) which is the correct formula for the area of a circle (assuming there is a typo and it's \( \pi r^{2} \) instead of \( \pi r^{3} \), maybe a formatting error in the original question, but among the given options, B is the closest to the correct formula for the area of a circle when considering possible typographical issues with the exponent).

Answer:

B. \( \pi r^{2} \) (assuming the exponent in option B is a typo and should be 2 instead of 3, as the area of a circle is \( A = \pi r^{2}\))