Fred took a ball that has a 13-inch diameter and drilled a circular hole through the centre of it. The hole was 5 inches wide, but how deep is it?
Answer
12 inches.
To solve this one, we can use the work of Pythagoras. If we draw the ball and hole from the side, they look like a circle with a rectangle in it, with all four points of the rectangle touching the circle.
We know the length of the short side and we need the length of the long side. To get it, we’ll need the length of the diagonal of the rectangle to create a triangle. By looking back at our drawing, we can see that the diagonal of the rectangle is equal to the diameter of the ball.
From that, we have a triangle where hypotenuse, c, is 13 inches, leg a is 5 inches, and we want to solve for leg b. Using c^2=a^2 + b^2, we solve for b and find that the depth of the hole is 12 inches.
