Final answer:
The volumes of the cylinder, cone, and pyramid are 254.34, 7, and 12 cubic units, respectively. The circumference and area of the circle are 14π inches and 49π square inches. Both penny stacks have a volume of 375 mm³.
Step-by-step explanation:
1. To find the volume of the cylinder with a diameter of 6 inches, we first find the radius, which is half the diameter (3 inches). The height is three times the radius, so the height is 9 inches. Using the formula V = πr²h, we have V = 3.14 * 3² * 9, which equals 254.34 cubic inches (rounded to the nearest hundredth).
2. the volume of a cone that fits perfectly inside the soda can is one third of the volume of the cylinder, since both the cone and the cylinder have the same height and radius. Therefore, the volume of the cone is 21 / 3, which is 7 cubic units.
3. the volume of the square pyramid that fits inside the cube with a volume of 36 cm³ is one third of the cube's volume when the base area of the pyramid is the same as the base area of the cube and the pyramid height equals the cube's side. Therefore, the pyramid's volume is 36 / 3, equaling 12 cm³.
4. For a circle with a diameter of 14 inches, we find the radius to be 7 inches. The circumference is C = 2πr, which is 14π inches, and the area is A = πr², which is 49π square inches.
5. The volume of the stack of pennies on the right is the same as the volume of the stack on the left if each stack contains the same number of pennies and each penny is identical. Therefore, the volume for the stack of pennies on the right is also 375 mm³.