Multiple choice

A solid wooden toy is in the form of a cone mounted on a hemisphere. If the radii of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of wood used in the toy.

  1. 343.72 cm3

  2. 266.11 cm3

  3. 532.22 cm3

  4. 133.55 cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius = 4.2 cm. Hemisphere volume = (2/3) * pi * 4.2^3 = 155.19. Cone height = 10.2 - 4.2 = 6 cm. Cone volume = (1/3) * pi * 4.2^2 * 6 = 110.84. Total = 155.19 + 110.84 = 266.03. Option B is the closest.

AI explanation

The total height of the toy is 10.2 centimeters, and since the radius of the hemisphere is 4.2 centimeters, the height of the cone is 10.2 minus 4.2 to equal 6 centimeters. The volume of the hemisphere is two-thirds multiplied by pi and the cube of 4.2, which evaluates to 155.232 cubic centimeters. The volume of the cone is one-third multiplied by pi, the square of 4.2 and 6, giving 110.88 cubic centimeters. Adding these two volumes together gives a total volume of 266.11 cubic centimeters.

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