Multiple choice

In a small town, Marcus, a famous craftsman known for his metalwork, was asked by the local community center to make a large hemispherical bowl for their annual festival. Marcus had a rectangular metal container lying around, measuring 5.5 meters long, 3 meters wide, and 1.176 meters high. He melted the metal and expertly shaped it into the desired hemispherical form. What would be the radius of that new hemispherical bowl Marcus had crafted? (Use π = 22/7)

  1. 1.4 m

  2. 2.1 m

  3. 2.8 m

  4. 3.5 m

  5. 4.0 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of rectangular container = 5.5 * 3 * 1.176 = 19.404 cubic meters. Volume of hemisphere = (2/3) * pi * r^3. (2/3) * (22/7) * r^3 = 19.404. (44/21) * r^3 = 19.404. r^3 = 19.404 * 21 / 44 = 9.261. r = cube root of 9.261 = 2.1.

AI explanation

The volume of the rectangular container is 5.5 times 3 times 1.176, which equals 19.404 cubic meters. Setting this equal to the volume of a hemisphere, (2 divided by 3) times pi times r cubed, gives (2 divided by 3) times (22 divided by 7) times r cubed equals 19.404. Solving for r cubed yields 9.261, and taking the cube root gives a radius of 2.1 meters.

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