A pipe has an outside diameter of 1.25 inches and an inside diameter of 0.75 inches. If Kelly hacksaws the pipe in two, what fraction of the pipe cross sectional area is sawn when the blade breaks through to the inside?

(1.25 - 0.75)/2 = 0.25

0.25/1.25 = 1/5

working backwards 3.25 0.75 1.25 3.75 what does that make

To determine the fraction of the pipe's cross-sectional area that is sawn when the blade breaks through to the inside, we need to calculate the areas of the outside and inside circles of the pipe.

The area of a circle can be calculated using the formula A = π * r^2, where A is the area and r is the radius.

First, let's determine the radii of the outside and inside circles. The outside diameter is given as 1.25 inches, so the radius of the outside circle is half of the diameter, which is 0.625 inches. Similarly, the inside diameter is given as 0.75 inches, so the radius of the inside circle is 0.375 inches.

Next, let's calculate the areas of the outside and inside circles.

Area of outside circle (A_outside) = π * (0.625 inches)^2 = π * 0.390625 square inches

Area of inside circle (A_inside) = π * (0.375 inches)^2 = π * 0.140625 square inches

Now, to find the fraction of the cross-sectional area that is sawn when the blade breaks through to the inside, we can subtract the area of the inside circle from the area of the outside circle and then divide by the area of the outside circle.

Fraction of cross-sectional area sawn = (A_outside - A_inside) / A_outside

= (π * 0.390625 square inches - π * 0.140625 square inches) / (π * 0.390625 square inches)

= (0.25 square inches) / (0.390625 square inches)

= 0.64 or 64%

So, when the blade breaks through to the inside, approximately 64% of the pipe's cross-sectional area is sawn.