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erica [24]
3 years ago
6

A cone has twice the base diameter and three-fourths the height of a cylinder. Can you tell what the relationship between the vo

lume of the cone and the volume of the cylinder is? Explain your reasoning.
Mathematics
1 answer:
Georgia [21]3 years ago
6 0

Answer:

Equal volumes

Step-by-step explanation:

Given

h \to height of cone

d \to diameter of cone

H \to height of cylinder

D \to diameter of cylinder

Such that:

d = 2D

h =\frac{3}{4}H

Required

The relationship between the volumes

The volume of a cylinder is:

V_1 = \pi R^2H

Where

R = 0.5D

So:

V_1 = \pi (0.5D)^2H

V_1 = \pi *0.25*D^2H

V_1 = 0.25\pi D^2H

The volume of the cone is:

V_2 = \frac{1}{3}\pi r^2h

Where

r =0.5d

r = 0.5 * 2D

r = D

and

h =\frac{3}{4}H

So, we have:

V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H

V_2 = \frac{1}{4}\pi * D^2H

V_2 = 0.25\pi * D^2H

V_2 = 0.25\pi D^2H

So, we have:

V_1 = 0.25\pi D^2H

V_2 = 0.25\pi * D^2H

V_1 = V_2

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