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A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and diameter of the base is 8 cm. Determine the volume of the toy. If the cube circumscribes the toy, then find the difference of the volumes of the cube and the toy. Also, find the total surface area of the toy.

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Answer:

See below ~

Step-by-step explanation:

Things to Find

  1. Volume of Toy
  2. Difference of Volumes in Cube and Toy
  3. Total Surface of Toy

Volume of Toy

  • Volume of Hemisphere + Volume (Cone)
  • 2/3πr³ + 1/3πr²h
  • 1/3πr² (2r + h)
  • 1/3 x 3.14 x 16 (8 + 4)
  • 1/3 x 50.24 x 12
  • 50.24 x 4
  • 200.96 cm³

Volume of Circumscribing Cube

  • Edge length is same as diameter
  • V = (8)³
  • V = 512 cm³

Difference in Volume

  • 512 - 200.96
  • 311.04 cm³

Slant height of cone

  • l² = 4² + 4²
  • l² = 32
  • l = 4√2 cm = 5.6 cm

Surface Area of Toy

  • CSA (hemisphere) + CSA (Cone)
  • 2πr² + πrl
  • πr (2r + l)
  • 3.14 x 4 (8 + 5.6)
  • 12.56 x 13.6
  • 170.8 cm²
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