SOLUTION: A solid metal ball has a volume of 1500 cm3
. It is melted to form a hollow spherical ball such that its interior diameter
is equal to the diameter of the original ball. What i
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Question 1169603: A solid metal ball has a volume of 1500 cm3
. It is melted to form a hollow spherical ball such that its interior diameter
is equal to the diameter of the original ball. What is the thickness of the resulting hollow spherical ball?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
The ball has volume 1500 cm^3
Let's find the radius of this ball.
V = (4/3)*pi*r^3
1500 = (4/3)*pi*r^3
3*1500 = 4pi*r^3
4500 = 4pi*r^3
4500/(4pi) = r^3
r^3 = 4500/(4pi)
r = (4500/(4pi))^(1/3)
r = 7.10124042307494
The radius of the ball is approximately 7.10124 cm
Now when we melt the ball down to form the hollow sphere, we are moving material around such that we form a hollow shell of some thickness such that this outer shell has volume V = 1500 cm^3. This outer shell combined with the inner spherical empty space of 1500 cm^3 makes a total volume of 1500+1500 = 3000 cm^3. Basically the volume has doubled.
Let's find the radius when V = 3000
V = (4/3)*pi*r^3
3000 = (4/3)*pi*r^3
3*3000 = 4pi*r^3
9000 = 4pi*r^3
9000/(4pi) = r^3
r^3 = 9000/(4pi)
r = (9000/(4pi))^(1/3)
r = 8.9470022893965
The new larger radius is approximately 8.94700 cm
Subtract the two radius values we found
8.9470022893965 - 7.10124042307494 = 1.84576186632156
The thickness is approximately 1.84576186632156 cm
Round this however you need to
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