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exis [7]
2 years ago
8

If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of con

e Rin terms of the radius of cylinder r is: ​

Mathematics
1 answer:
olga nikolaevna [1]2 years ago
5 0

Answer: R = √(3*r^2)

Step-by-step explanation:

For a cylinder with radius r and height H, the volume is:

V = pi*r^2*H

For a cone of height H, and with a base of radius R, the volume is:

V = (1/3)*pi*R^2*H

In this case, we know that both figures have the same height, and the same volume, then we can write:

pi*r^2*H = (1/3)*pi*R^2*H

Now we can divide by pi in both sides to get:

(pi*r^2*H)/pi = ((1/3)*pi*R^2*H)/pi

r^2*H = (1/3)*R^2*H

Now we can divide both sides by H:

(r^2*H)/H = ((1/3)*R^2*H)/H

r^2 = (1/3)*R^2

Now we want to write R in terms of r.

Then we need to isolate R in the above equation:

r^2 = (1/3)*R^2

3*r^2 = R^2

√(3*r^2) = R

R = √(3*r^2)

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