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A prism has a height of 5 inches and a volume of 80 cubic inches. Select all figures that could be the base for this prism. A. A2-inch-by-8-inch rectangle B. A circle with radius 2 inches C. A heart-shaped base with an area of 16 square inches D. A square with side length 4 inches. E. A right triangle with legs 4 inches long

A prism has a height of 55 inches and a volume of 8080 cubic inches. Select all figures that could be the base for this prism.\newlineA. A22-inch-by−8-8-inch rectangle\newlineB. A circle with radius 22 inches\newlineC. A heart-shaped base with an area of 1616 square inches\newlineD. A square with side length 44 inches.\newlineE. A right triangle with legs 44 inches long

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Q. A prism has a height of 55 inches and a volume of 8080 cubic inches. Select all figures that could be the base for this prism.\newlineA. A22-inch-by−8-8-inch rectangle\newlineB. A circle with radius 22 inches\newlineC. A heart-shaped base with an area of 1616 square inches\newlineD. A square with side length 44 inches.\newlineE. A right triangle with legs 44 inches long
  1. Volume Formula Application: The volume of a prism is given by the formula V=BhV = Bh, where BB is the area of the base and hh is the height of the prism. We are given that the height (hh) is 55 inches and the volume (VV) is 8080 cubic inches. We can use this information to find the required area of the base (BB) by rearranging the formula to B=VhB = \frac{V}{h}.
  2. Base Area Calculation: Using the formula B=VhB = \frac{V}{h}, we substitute the given values to find the area of the base.B=80 cubic inches5 inches=16 square inches.B = \frac{80 \text{ cubic inches}}{5 \text{ inches}} = 16 \text{ square inches}.The area of the base must be 16 square inches16 \text{ square inches} for the prism to have a volume of 80 cubic inches.80 \text{ cubic inches}.
  3. Option Evaluation: Square: Now we will check each option to see if the area of the base matches 1616 square inches.\newlinea. A square with side length 44 inches.\newlineThe area of a square is given by A=side2A = \text{side}^2. For a square with side length 44 inches, the area is A=42=16A = 4^2 = 16 square inches.
  4. Option Evaluation: Rectangle: b. A 22-inch-by-88-inch rectangle.\newlineThe area of a rectangle is given by A=length×widthA = \text{length} \times \text{width}. For a rectangle with length 88 inches and width 22 inches, the area is A=8×2=16A = 8 \times 2 = 16 square inches.
  5. Option Evaluation: Circle: c. A circle with radius 22 inches.\newlineThe area of a circle is given by A=πr2A = \pi r^2. For a circle with radius 22 inches, the area is A=π×22=π×4≈12.57A = \pi \times 2^2 = \pi \times 4 \approx 12.57 square inches, which is not equal to 1616 square inches.
  6. Option Evaluation: Heart: e. A heart-shaped base with an area of 1616 square inches.\newlineThe area is explicitly given as 1616 square inches, which matches the required area for the base of the prism.
  7. Option Evaluation: Triangle: d. A right triangle with legs 44 inches long.\newlineThe area of a right triangle is given by A=(1/2)×base×heightA = (1/2) \times \text{base} \times \text{height}. For a right triangle with legs 44 inches long, the area is A=(1/2)×4×4=8A = (1/2) \times 4 \times 4 = 8 square inches, which is not equal to 1616 square inches.

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