Amy is creating an enlargement of the following image for an art gallery. She needs the enlargement to follow the scale of ¼ of a foot to 3 feet. This will result in an image with a length of 8 feet and width of 6 feet.

what is the unit rate of area in square feet of the enlargement image per square foot of area of the original image?

A. 144 square feet per square foot

B. 48 square feet per square foot

C. 16 square feet per square foot

D. 32 square feet per square foot

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)