Problem 28 - Elementary Algebra

Question

The diameter of a circular saw blade is 3.375 in. Find its area. Round to the nearest tenth.

Step-by-Step Solution

Answer

The area is 8.9 square inches.

Step 1: Find the Radius

The radius of a circle is half of its diameter. Given the diameter of the circular saw blade is 3.375 inches, divide it by 2 to find the radius.Radius = Diameter / 2Radius = 3.375 / 2 = 1.6875 inches

Step 2: Write the Area Formula

The formula for the area of a circle is A = πr^2where A is the area, π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle.

Step 3: Substitute the Radius into the Formula

Now that the radius is known, substitute 1.6875 inches into the area formula to find the area:A = π(1.6875)^2

Step 4: Calculate the Area

First, calculate the square of the radius:(1.6875)^2 ≈ 2.84765625Then multiply by π:A ≈ 3.14159 * 2.84765625 ≈ 8.944

Step 5: Round to the Nearest Tenth

Finally, round the area to the nearest tenth. The calculated area 8.944 rounded to the nearest tenth is 8.9 square inches.

Key Concepts

radius calculation

To find the area of a circle, the first step is to determine the radius. The radius is simply half of the diameter.
In our exercise, the diameter of the circular saw blade is given as 3.375 inches. To calculate the radius, we divide the diameter by 2:

• Radius = Diameter / 2
• Radius = 3.375 / 2 = 1.6875 inches

This gives us a radius of 1.6875 inches. This value is vital for the next steps in solving for the area.

area formula

The area of a circle can be determined using a specific formula. The area formula for a circle is given by:
A = πr^2

Where:

• A is the area
• π (pi) is a mathematical constant approximately equal to 3.14159
• r is the radius of the circle

Using this formula requires knowledge of the radius, which we calculated in the previous section.
Plugging in the radius of 1.6875 inches into the formula, we get:Area ≈ 3.14159 * (1.6875)^2

rounding numbers

Once you have calculated the area using the formula, the last step often involves rounding the result to make it more readable.
In our example:
(1.6875)^2 ≈ 2.84765625
Multiplying this by π gives us:
3.14159 * 2.84765625 ≈ 8.944
To round to the nearest tenth, look at the first digit after the decimal point. If it is 5 or greater, round up. If it is less than 5, round down.
Here, 8.944 rounds to 8.9 because the number 4 (in the tenths place) dictates that we round down.
This gives us a final area of approximately 8.9 square inches.