Multiple choice

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted to form a solid cylinder of base diameter 8 cm. What is the height of the cylinder?

  1. 4.5 cm

  2. 4.67 cm

  3. 4.7 cm

  4. 3.67 c

  5. 4.56 c
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The hollow sphere volume is (4/3)pi(4^3 - 2^3) = (224/3)pi. Equating this to the cylinder volume pi(4^2)h gives h = 14/3 cm, approximately 4.67 cm.

AI explanation

By the volume conservation method, the volume of the hollow sphere equals the volume of the resulting solid cylinder. The internal and external radii of the sphere are 2 cm and 4 cm respectively, so its volume is 4/3 times pi times (4 cubed minus 2 cubed), giving 224/3 times pi cubic centimeters. Using the cylinder volume formula V equals pi times r squared times height with a base radius of 4 cm, we have 224/3 times pi equals pi times 4 squared times height; solving for height yields 224 divided by 48, which is 4.67 cm.

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