Question The diameter of a circle is 15 cm . Find its area to the nearest whole number.

Question

UpStudy AI · Accepted Answer

$$
\textbf{Step 1: Identify the radius.}
$$

The radius is half of the diameter. Given the diameter is 15 cm, the radius $$ r $$ is:

$$
r = \frac{15}{2} = 7.5 \text{ cm}
$$

$$
\textbf{Step 2: Write down the formula for the area of a circle.}
$$

The formula for the area $$ A $$ of a circle is:

$$
A = \pi r^2
$$

$$
\textbf{Step 3: Substitute the radius into the formula.}
$$

Substitute $$ r = 7.5 \text{ cm} $$:

$$
A = \pi (7.5)^2
$$

$$
\textbf{Step 4: Compute the value of }(7.5)^2.
$$

$$
(7.5)^2 = 56.25
$$

Thus,

$$
A = \pi \times 56.25
$$

$$
\textbf{Step 5: Calculate the area using } \pi \approx 3.1416.
$$

$$
A \approx 3.1416 \times 56.25 \approx 176.7146 \text{ cm}^2
$$

$$
\textbf{Step 6: Round the area to the nearest whole number.}
$$

Rounding $$ 176.7146 $$ to the nearest whole number gives:

$$
A \approx 177 \text{ cm}^2
$$

$$
\boxed{177 \text{ cm}^2}
$$
The area of the circle is approximately 177 cm².

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