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Chapter 1: Problem 14

Find the area of a circle with a diameter of \(8 \mathrm{~m}\).

Short Answer

Expert verified
The area is \(16\pi \mathrm{~m}^2\).

Step by step solution

01

Title - Find the radius

To find the area of a circle, start by finding the radius. The radius is half the diameter. Since the diameter is given as 8 meters, divide by 2 to get the radius: \(r = \frac{8}{2} = 4 \mathrm{~m}\).
02

Title - Use the Area Formula

The formula for the area of a circle is \(A = \pi r^2\). Plug the radius found in Step 1 into this formula: \(A = \pi (4)^2\).
03

Title - Calculate the Area

Now, calculate the area by squaring the radius and multiplying by \(\pi\): \(A = \pi (16) = 16\pi \mathrm{~m}^2\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radius Calculation
To find the area of a circle, you first need to know its radius. The radius is the distance from the center of the circle to any point on its edge. If you know the diameter, which is the distance across the circle passing through the center, you can find the radius easily.
For example, if a circle's diameter is 8 meters, you can find the radius by dividing the diameter by 2. So, the radius will be:
\(\r = \frac{8}{2} = 4 \text{ meters} \).
The radius is a crucial part of calculating the area of a circle because the area formula uses the radius as one of its components.
Circle Area Formula
The formula to find the area of a circle is centered around \(\pi\), which is a constant approximately equal to 3.14159. The area formula is:
\(\text{A} = \pi r^2 \).
Here, \(\text{A} \) represents the area of the circle, while \(r \) represents the radius of the circle.
This formula tells you that you need to square the radius first, and then multiply the result by \(\pi\).
Let's put this into practice with our radius of 4 meters:
\(\text{A} = \pi (4)^2\).
Squaring a Number
Squaring a number means multiplying that number by itself. It's a key step in many math problems, including finding the area of a circle.
When the radius of the circle is 4 meters, squaring the radius means calculating: \br> \(4 \times 4 = 16\).
So, \(4^2 = 16\).
Now you take this squared value in the area formula:
\(\text{A} = \pi (16)\).
This finally gives us:
\( \text{A} = 16 \pi \, \text{ or approximately } 50.27 \text{ square meters (using } \pi=3.14159 \text{).}\).
Breaking down each step can help you grasp the entire process easily!

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Most popular questions from this chapter

Find the volume of a cone with a radius of 6 in. and a height of 11 in.

\(\frac{2}{3}(6 x-8)-\frac{7}{10} x+4\)

The diameter of a circular bathroom sink is 15.75 in. Find its circumference. Round to the nearest hundredth.

Find the area of a circle with a diameter of \(12 \mathrm{~m}\).

Find the volume of a cylinder with a diameter of 11 in. and a height of 27 in.
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