SOLUTION: A solid cylinder dear 8 cm long and of 3.5 cm radius is melted to form a hollow cylinder is melted to form a hollow cylinder of external radius 4 cm and 1 cm thi knees . What is le

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Question 1011498: A solid cylinder dear 8 cm long and of 3.5 cm radius is melted to form a hollow cylinder is melted to form a hollow cylinder of external radius 4 cm and 1 cm thi knees . What is length of hollow cylinder
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A solid cylinder dear 8 cm long and of 3.5 cm radius is melted to form a hollow cylinder is melted to form a hollow cylinder of external radius 4 cm and 1 cm thi knees . What is length of hollow cylinder

A solid cylinder dear 8 cm long and of 3.5 cm radius is melted to form a hollow cylinder is melted to form a hollow cylinder of external radius 4 cm and 1 cm thiCKNESS knees . What is length of hollow cylinder ?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
volume of a cylinder = pi*r^2*h

the solid cylinder volume = pi*3.5^2*8 = pi*98

the hollow cylinder has an external radius of 4 cm and an internal radius of 3 cm.

if you subtract the volume of the cylinder with 3 cm radius from the volume of the cylinder with 4 cm radius, you are left with a cylinder that has a wall of 1 cm width.

the material from the solid cylinder is then poured into this wall to make it solid.

the height is calculated from the following measurements.

the material that will be poured into the wall to make it solid has a volume of 98*pi.

the volume of the cylinder with the radius of 4 cm = pi*4^2*h = 16*pi*h.

the volume of the cylinder with the radius of 3 cm = pi*3^3*h = 9*pi*h.

subtract 9*pi*h from 16*pi*h and you have a wall wall that is 1 cm thick and has a volume of 7*pi*h.

you determine the height of this wall by solving the following equation.

7*pi*h = 98*pi

divide both sides of this equation by 7*pi to get h = 98*pi / (7*pi).

solve for h to get h = 14 cm.

here's a picture of what i mean.

not the best, but hopefully good enough.

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