Two spheres are cut from a certain uniform rock. One has radius 4.75 cm. The mass of the other is three times greater. Find its radius.

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- Aug 31st 2008, 09:19 PM #1

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- Sep 1st 2008, 12:12 AM #2

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Same piece of rock of uniform density.

density = (mass) / (volume)

4/3*

So, if density is constant or the same,

(m1)/(V1) = (m2)/(V2)

where V1 is volume of m1

and V2 is volume of m2

Given: m2 = 3*m1

So,

(m1)/(V1) = (3*m1)/V2

1 /V1 = 3 /V2

Cross multiply,

V2 = 3*V1

Let R = radius of m2,

(4/3)pi(R^3) = 3[(4/3)pi(4.75)^3]

R^3 = 3(4.75)^3

R = (4.75)cubrt(3) cm -------answer.

In decimals,

R = 6.8507 cm -------answer also

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