How far from its center should a grapefruit with a 6-inch diameter be sliced, in order that both circular sections have the same radius as the two halves of a perfectly sliced orange with a 4-inch diameter?
nice math, but you didn't answer the question.
draw a side view. The slice is x inches from the center, and has a radius of 2. The grapefruit has a radius of 3, so
x^2 + 2^2 = 3^2
x = √5 inches
Apologies for the oversight. You are correct.
To find the distance 'x' from the center of the grapefruit slice where both circular sections have the same radius as the two halves of a perfectly sliced orange, we can use the Pythagorean theorem.
Let's draw a side view of the grapefruit. The grapefruit has a radius of 3 inches, and the slice is 'x' inches away from the center. The circular section formed by one of the slices has a radius of 2 inches.
Using the Pythagorean theorem, we can set up the following equation:
x^2 + 2^2 = 3^2
Simplifying:
x^2 + 4 = 9
Subtracting 4 from both sides:
x^2 = 5
Taking the square root of both sides:
x = √5 inches
Therefore, the grapefruit should be sliced approximately √5 inches from its center in order for both circular sections to have the same radius as the two halves of a perfectly sliced orange with a 4-inch diameter.
To find out how far from the center the grapefruit should be sliced, we can use the concept of similar triangles.
Let's assume that the radius of the orange is r inches. Since the diameter of the orange is 4 inches, the radius can be calculated as r = 4/2 = 2 inches.
Now, let's consider the grapefruit. The diameter of the grapefruit is 6 inches, so its radius is r + x, where x represents the distance from the center of the grapefruit to the slice.
We can create a similar triangle between the orange and the grapefruit. Since both triangles share a common vertex at the center of the fruit and have two congruent angles, they are similar.
Using the property of similar triangles, we can set up the following proportion:
(r + x) / r = 6 / 4
Now, we can solve this proportion for x:
4(r + x) = 6r
4r + 4x = 6r
4x = 2r
x = 2r / 4
Simplifying further,
x = r / 2
Since we know that r = 2 inches, we can substitute this value:
x = 2 / 2
x = 1 inch
Therefore, the grapefruit should be sliced 1 inch away from its center to create two circular sections with the same radius as the two halves of a perfectly sliced orange with a 4-inch diameter.
To determine how far from the center the grapefruit should be sliced, we need to compare the radii of the circular sections of the grapefruit to the radius of the halves of a perfectly sliced orange.
Let's start by finding the radius of the grapefruit. The diameter of the grapefruit is given as 6 inches. The formula to find the radius (r) from the diameter (d) is: r = d/2.
Applying the formula, the radius of the grapefruit is:
r = 6 inches / 2 = 3 inches.
Next, we need to find the radius of the halves of the orange. The diameter of the orange is given as 4 inches. Applying the same formula, we find:
r = 4 inches / 2 = 2 inches.
Now, we need to figure out how far from the center the grapefruit should be sliced so that the circular sections have the same radius as the halves of the orange.
Since we want both circular sections to have a radius of 2 inches, we need to calculate the distance from the center of the grapefruit to the slice. Let's call this distance "x".
If we subtract the radius of the orange halves (2 inches) from the radius of the grapefruit (3 inches), we get the remaining distance, which is x:
x = 3 inches - 2 inches = 1 inch.
Therefore, the grapefruit should be sliced 1 inch away from its center in order for both circular sections to have the same radius as the halves of a perfectly sliced orange.
To solve this problem, we can use the concept of similar triangles formed by the radii of the grapefruit and the orange.
Let's assume the grapefruit is sliced at a distance 'x' from its center. The radius of the smaller circular section formed by one of the slices will be 'x'. We need to find this value of 'x'.
The radius of the grapefruit is half its diameter, which is 6/2 = 3 inches. The radius of the orange is half its diameter, which is 4/2 = 2 inches.
Using the concept of similar triangles, we can set up the following proportion:
orange radius / orange diameter = grapefruit radius / grapefruit diameter
2 / 4 = x / 2x
Cross-multiplying:
2 * 2x = 4 * x
4x = 4x
This equation states that the ratio of the radius to diameter is the same for both the orange and the grapefruit slices. Therefore, we can conclude that the two circular sections formed by slicing the grapefruit should have the same radius when x = 2 inches.
So, a grapefruit with a 6-inch diameter should be sliced 2 inches from its center in order for both circular sections to have the same radius as the two halves of a perfectly sliced orange with a 4-inch diameter.