Multiple choice

Find the volume of a shape obtained by placing a cone onto the circular end of hemisphere. The hemisphere has a radius $5$ cm and height of the cone is $4$ cm.

  1. $266.5\ cm^{3}$
  2. $366.5\ cm^{3}$
  3. $456.5\ cm^{3}$
  4. $576.5\ cm^{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume = Volume of hemisphere + Volume of cone. V = (2/3)pi*r^3 + (1/3)pi*r^2*h. r=5, h=4. V = (2/3)pi(125) + (1/3)pi(25)(4) = (250/3)pi + (100/3)pi = (350/3)pi. (350/3) * 3.14159 = 366.519.

AI explanation

The volume of a hemisphere is given by the formula V = (2/3) * pi * r^3, so for a radius of 5 cm, the volume is (2/3) * pi * 5^3, which is 250/3 * pi cubic cm or approximately 261.67 cubic cm. The volume of a cone is V = (1/3) * pi * r^2 * h, so for a radius of 5 cm and a height of 4 cm, the volume is (1/3) * pi * 5^2 * 4, which equals 100/3 * pi cubic cm or approximately 104.67 cubic cm. Adding these two volumes together, 261.67 + 104.67 gives a total volume of 366.5 cubic cm.

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