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.
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?
3 answers
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
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 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.