The diameter of a spherical grapefruit is 6.0 inches. An amateur fruit slicer misses its center by one inch. What is the radius of the circular slice?
draw a side view.
Draw a circle
Mark a vertical diameter
Draw a horizontal radius from the center O
The radius has length 3
Draw another vertical line 1 unit away from the center.
On that vertical line, mark its intersections with the horizontal radius (A) and the circle (B).
Then you have a right triangle OAB.
OA^2 + AB^2 = OB^2
1^2 + AB^2 = 3^2
AB^2 = 8
AB = √8
Note that AB is the radius of the sliced section.
this is sooooo useful
Well, the amateur fruit slicer seems to have pulled a "slicer's remorse" and missed the center! To find the radius of the circular slice, we first need to determine how far the amateur slicer has gone "off-center". Since the diameter of the grapefruit is 6.0 inches, missing the center by one inch means the slicer is actually cutting at a radius of 6/2 - 1 = 2.0 inches. So, the radius of the circular slice is 2.0 inches. Remember, next time, aim for the bullseye!
The radius of a sphere is half of its diameter. So, the radius of the grapefruit is 6.0 inches / 2 = <<6.0/2=3.0>>3.0 inches.
Since the amateur fruit slicer missed the center by one inch, the radius of the circular slice is the radius of the grapefruit minus one inch.
Therefore, the radius of the circular slice is 3.0 inches - 1.0 inch = <<3.0-1.0=2.0>>2.0 inches.
To find the radius of the circular slice, we need to know the distance from the center of the grapefruit to the edge of the slice.
Given that the diameter of the grapefruit is 6.0 inches, we can calculate the radius by dividing the diameter by 2. So the radius of the grapefruit is 6.0 inches / 2 = 3.0 inches.
Since the amateur fruit slicer misses the center by one inch, the distance from the center of the grapefruit to the edge of the slice is equal to the radius of the grapefruit minus one inch. Thus, the radius of the circular slice is 3.0 inches - 1.0 inch = 2.0 inches.