1. What is the area of a square part that measures 3 inches by 3 inches? 2. What is the area of a screw that has a two-inch diameter? (Round to the second decimal point)
Understand the Problem
There are two questions present. The first question asks for the area of a square with sides of 3 inches. This requires multiplying the side length by itself. The second question asks for the area of a circle (since a screw is circular) with a diameter of 2 inches. This requires using the formula area = pi * radius^2.
Answer
9 in² 3. 14 in²
Answer for screen readers
9 in² 3. 14 in²
Steps to Solve
- Calculate the area of the square
To find the area of a square, we multiply the side length by itself. Since the square measures 3 inches by 3 inches, the area is $3 \times 3$.
- Compute the area
$3 \times 3 = 9$ The area of the square is 9 square inches.
- Determine the radius of the circle
The diameter of the circle (screw) is given as 2 inches. The radius is half of the diameter. Therefore, the radius $r$ is $2/2 = 1$ inch.
- Calculate the area of the circle
The formula for the area of a circle is $A = \pi r^2$, where $r$ is the radius. Substitute $r = 1$ into the formula: $A = \pi (1)^2 = \pi$.
- Approximate $\pi$ to two decimal places
We know that $\pi \approx 3.14159$. Rounded to two decimal places, this is 3.14. Therefore, the area of the circle is approximately 3.14 square inches.
9 in² 3. 14 in²
More Information
The value of $\pi$ is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159.
Tips
A common mistake is to use the diameter instead of the radius in the area formula for the circle. Another mistake is to not round to the required number of decimal places, or to round incorrectly. For the square, a common mistake may include adding the sides instead of multiplying. In the area of the circle, one might forget that the formula includes squaring the radius.
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