Determine and state the number of full cones of water needed to completely fill the cylinder with water.
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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.

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University of Lagos Nigeria
23 June 2020

University of Benin Nigeria
23 June 2020
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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)

= 96π

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)

= 12π

Therefore, N = 96π / 12π

= 8

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