In the diagram below, a right circular cone with a radius of 3 inches has a slant height of 5 inches, and a right cylinder with a radius of 4 inches has a height of 6 inches.
Determine and state the number of full cones of water needed to completely fill the cylinder with water.
Number of full cones of water needed to completely fill the cylinder with water, N = Volume of Cylinder, V1 / Volume of Cone, V2.
That is, N = V1/V2
V1 = πr12h1
where r1 and h1 are the radius and height of the cylinder respectively.
V1 = π(4)2(6)
V2 = 1/3 πr22h2
Where r2 and h2 are radius and vertical height of the cone respectively.
From pythagorean's theorem, h2 = 52 - 32
h22 = 25 - 9
h22 = 16
Take square root of both sides
h2 = 4
Thus, V2 = 1/3 π(3)2(4)
Therefore, N = 96π / 12π