SOLUTION: In the process of making a sphere out of marble, the first step is to cut the rough piece of marble into a cube. After this, rough cuts are made to get rid of as many corners as p
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Question 1037678: In the process of making a sphere out of marble, the first step is to cut the rough piece of marble into a cube. After this, rough cuts are made to get rid of as many corners as possible. Then, the sculptor grinds away any sharp edges. The result is a roundish piece of rock that is put into another grinding machine that has two cupped grinders rotating in opposite directions.
a. What volume of rock was in the cube if the original piece of rock was cut into a cube with side lengths of 60 mm? Round to the nearest cubic millimetre.
b. What is the maximum diameter of the sphere that could be made from the cube?
c. If the sphere has the maximum diameter, what is the volume of rock in the sphere at the end of the process? Round to the nearest cubic millimetre.
d. How much rock was cut or ground away?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In the process of making a sphere out of marble, the first step is to cut the rough piece of marble into a cube. After this, rough cuts are made to get rid of as many corners as possible. Then, the sculptor grinds away any sharp edges. The result is a roundish piece of rock that is put into another grinding machine that has two cupped grinders rotating in opposite directions.
a. What volume of rock was in the cube if the original piece of rock was cut into a cube with side lengths of 60 mm? Round to the nearest cubic millimetre.
Ans: 60^3 = 216000 mm^3
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b. What is the maximum diameter of the sphere that could be made from the cube?
Ans: 60mm
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c. If the sphere has the maximum diameter, what is the volume of rock in the sphere at the end of the process? Round to the nearest cubic millimetre.
V = (4/3)pi*r^3
V = (4/3)pi*30^3 = 113,097 mm^3
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d. How much rock was cut or ground away?
216000- 113.097 = 102,903 mm^3
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Cheers,
Stan H.
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