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Find the volume of an object with a base that is a circle of radius 22 and cross sections that are squares

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Full solution

Q. Find the volume of an object with a base that is a circle of radius 22 and cross sections that are squares
  1. Calculate base area: The base is a circle with radius r=2r = 2. The area of the base, AA, is A=πr2A = \pi r^2.\newlineCalculate the area: A=π(2)2=4πA = \pi(2)^2 = 4\pi.
  2. Calculate side length: Each cross section of the object is a square. The side length of each square is equal to the diameter of the base circle.\newlineCalculate the side length: Diameter =2×radius=2×2=4= 2 \times \text{radius} = 2 \times 2 = 4.
  3. Calculate square area: The area of each square cross section is the side length squared.\newlineCalculate the area of the square: Areasquare=side_length2=42=16\text{Area}_{\text{square}} = \text{side\_length}^2 = 4^2 = 16.
  4. Calculate volume: The volume of the object is the area of the base multiplied by the height. In this case, the height is the same as the side length of the square cross section.\newlineCalculate the volume: Volume = A×height=4π×4A \times \text{height} = 4\pi \times 4.

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