Question

1. the area of a circle with radius r is given by the formula $a = \pi r^2$. if the radius of a circle is 7.5 centimeters, what is the area of the circle to the nearest hundredth? (use $\pi = 3.14$)

a) $176.63\\ \text{cm}^2$ b) $706.50\\ \text{cm}^2$ c) $47.10\\ \text{cm}^2$ d) $168.75\\ \text{cm}^2$

Explanation:

Step1: Identify the formula and values

We know the formula for the area of a circle is \( A=\pi r^{2} \), where \( r = 7.5 \) cm and \( \pi=3.14 \).

Step2: Substitute the values into the formula

First, calculate \( r^{2} \): \( r^{2}=(7.5)^{2}=7.5\times7.5 = 56.25 \).
Then, multiply by \( \pi \): \( A = 3.14\times56.25 \).

Step3: Perform the multiplication

\( 3.14\times56.25=176.625 \).

Step4: Round to the nearest hundredth

Rounding \( 176.625 \) to the nearest hundredth gives \( 176.63 \).

Answer:

A) \( 176.63\space cm^{2} \)