If the radius of a circle is 7.4., what is the area of the circle?
The correct answer and explanation is:
specific unit is given for the radius, we state the area in generic “square units”.
Therefore, a circle with a radius of 7.4 has an area of approximately 171.98 square units.Okay, here is the calculation for the area of the circle and the explanation.
Correct Answer:
The area of the circle with a radius of 7.4 is approximately 172.03 square units.
Explanation (approximately 300 words):
To find the area of a circle, we use a specific mathematical formula that relates the radius of the circle to the space it occupies. The formula for the area of a circle is:
Area = π * r²
Where:
Area is the space inside the circle.
π (pi) is a mathematical constant, approximately equal to 3.14159. It represents the ratio of a circle’s circumference to its diameter.
r is the radius of the circle, which is the distance from the center of the circle to any point on its edge.
r² means the radius multiplied by itself (radius squared).
In this problem, we are given that the radius (r) of the circle is 7.4.
First, we need to square the radius:
r² = 7.4 * 7.4
Let’s calculate 7.4 multiplied by 7.4:
7.4
x 7.4
296 (4 * 74)
5180 (70 * 74)
54.76
So, r² = 54.76.
Now, we plug this value back into the area formula and multiply it by π:
Area = π * 54.76
Using the approximate value of π (around 3.14159), we perform the multiplication:
Area ≈ 3.14159 * 54.76
Using a calculator for better precision:
Area ≈ 172.03361…
We can round this result to a couple of decimal places for practical purposes. Rounding to two decimal places, we get 172.03.
Therefore, the area of the circle with a radius of 7.4 is approximately 172.03 square units. Remember that area is always measured in square units, such as square inches, square centimeters, or simply “square units” if no specific unit is provided for the radius.