Multiple choice

A wooden toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm.Determine the volume of the toy.

  1. $94.29\, cm^3$
  2. $108.25\, cm^3$
  3. $48.52\, cm^3$
  4. $90.28\, cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume = Volume of hemisphere + Volume of cone. V = (2/3)pi*r^3 + (1/3)*pi*r^2*h. r=3, h=4. V = (1/3)*pi*r^2(2r + h) = (1/3)3.14*9(6+4) = 3*3.14*10 = 94.2 cm^3. The option 94.29 is the closest.

AI explanation

The common radius is half the diameter, which is three centimeters. The volume of the toy is the sum of the volume of the hemisphere, which is two by three pi r cubed, and the volume of the cone, which is one by three pi r squared h. Substituting the values gives the total volume as two by three pi times three cubed plus one by three pi times three squared times four, which simplifies to eighteen pi plus twelve pi, equaling thirty pi. Taking pi as twenty two by seven gives thirty times twenty two by seven, resulting in ninety four point two nine cubic centimeters.