Answer :
Sure! Let's work through the solution step by step.
Part A: Finding the Radius
1. We know the diameter of the grapefruit slice is 6.2 inches.
2. The radius is half of the diameter. So, to find the radius, we divide the diameter by 2.
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{6.2}{2} = 3.1 \text{ inches}
\][/tex]
So, the radius of the grapefruit slice is 3.1 inches.
Part B: Calculating the Area
1. The formula for the area of a circle is [tex]\( \pi \times \text{radius}^2 \)[/tex].
2. We've found the radius to be 3.1 inches, and we'll use 3.14 for [tex]\( \pi \)[/tex].
3. Plug these values into the formula:
[tex]\[
\text{Area} = 3.14 \times (3.1)^2
\][/tex]
4. Calculate the radius squared:
[tex]\[
(3.1)^2 = 9.61
\][/tex]
5. Multiply by [tex]\( \pi \)[/tex] (3.14):
[tex]\[
\text{Area} = 3.14 \times 9.61 = 30.1754
\][/tex]
6. Round the area to the nearest tenth:
[tex]\[
\text{Area} \approx 30.2
\][/tex]
So, the area of the grapefruit slice is approximately 30.2 square inches.
Part A: Finding the Radius
1. We know the diameter of the grapefruit slice is 6.2 inches.
2. The radius is half of the diameter. So, to find the radius, we divide the diameter by 2.
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{6.2}{2} = 3.1 \text{ inches}
\][/tex]
So, the radius of the grapefruit slice is 3.1 inches.
Part B: Calculating the Area
1. The formula for the area of a circle is [tex]\( \pi \times \text{radius}^2 \)[/tex].
2. We've found the radius to be 3.1 inches, and we'll use 3.14 for [tex]\( \pi \)[/tex].
3. Plug these values into the formula:
[tex]\[
\text{Area} = 3.14 \times (3.1)^2
\][/tex]
4. Calculate the radius squared:
[tex]\[
(3.1)^2 = 9.61
\][/tex]
5. Multiply by [tex]\( \pi \)[/tex] (3.14):
[tex]\[
\text{Area} = 3.14 \times 9.61 = 30.1754
\][/tex]
6. Round the area to the nearest tenth:
[tex]\[
\text{Area} \approx 30.2
\][/tex]
So, the area of the grapefruit slice is approximately 30.2 square inches.
