Question

to the nearest hundredth, what is the area of a circle with a radius of 5 units?

a. 64.57 square units

b. 15.71 square units

c. 31.42 square units

d. 78.54 square units

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Substitute the given radius into the formula

We are given that the radius \( r = 5 \) units. Substituting this into the formula, we get \( A=\pi\times(5)^2 \).

Step3: Calculate the value

First, calculate \( 5^2 = 25 \). Then, multiply by \( \pi \) (using \( \pi\approx3.14159 \)): \( A = 3.14159\times25 = 78.53975 \).

Step4: Round to the nearest hundredth

Rounding \( 78.53975 \) to the nearest hundredth gives \( 78.54 \).

Answer:

D. 78.54 square units