A large pizza has a diameter of 9 inches. Which of the following is the area of the pizza in terms of pi ()?
A.
11.25 πin2
B.
29.57 πin2
C.
18.35 πin2
D.
20.25 πin2
The Correct answer and Explanation is:
To solve for the area of the pizza in terms of π\piπ, we need to use the formula for the area of a circle, which is:Area=πr2\text{Area} = \pi r^2Area=πr2
Here, rrr is the radius of the circle. The problem states that the pizza has a diameter of 9 inches. The radius rrr is half of the diameter, so:r=9 inches2=4.5 inchesr = \frac{9 \text{ inches}}{2} = 4.5 \text{ inches}r=29 inches=4.5 inches
Next, we substitute the radius into the area formula:Area=π(4.5)2\text{Area} = \pi (4.5)^2Area=π(4.5)2
Now, calculate 4.524.5^24.52:4.52=4.5×4.5=20.254.5^2 = 4.5 \times 4.5 = 20.254.52=4.5×4.5=20.25
So, the area of the pizza is:Area=20.25π square inches\text{Area} = 20.25\pi \text{ square inches}Area=20.25π square inches
Thus, the correct answer is:
D. 20.25 π\piπ in2^22
Explanation:
The area of a circle is determined by the formula πr2\pi r^2πr2, where rrr is the radius. The diameter of a circle is twice the radius, so when given the diameter, you must divide it by 2 to find the radius. In this case, the pizza’s diameter is 9 inches, so the radius is 4.54.54.5 inches. Squaring the radius gives us 20.2520.2520.25 square inches. Therefore, the area of the pizza is 20.25π20.25\pi20.25π square inches.
This problem tests your understanding of the relationship between the diameter, radius, and area of a circle. It also requires you to correctly apply the formula for the area, substituting the radius and ensuring that the calculation of the square of the radius is accurate. By understanding these steps, you can confidently determine the area of any circle, as long as you know either the radius or the diameter.