4. an investigator at a crime scene found a triangular piece of torn fabric. the investigator remembered that one of the
suspects had a triangular hole in their coat. perhaps it was a match. unfortunately, to avoid tampering with evidence, the
investigator did not want to touch the fabric and could not fit it to the coat directly. what would the investigator need to
measure from the torn piece of fabric and/or the hole in the coat to determine if the torn fabric could have come from the
coat?
99

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)