Lupe’s construction is building a rectangular house that is 16 feet longer than it is wide. they will be putting a 3-foot wide sidewalk all the way around the house. there will be a protective metal strip around the outside edge of the sidewalk. if the house will have a perimeter of 136 feet, how will the four pieces of the protective strip need to be

Proving the congruent supplements theorem

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)

The ideal weight of a nickel is 0.176 ounce. to check that there are 40 nickels in a roll, a bank weighs the roll and allows for an error of 0.015 ounce in total weight