SOLUTION: A rocket consists of a right circular cylinder of height 20 m surmounted by a cone whose height and diameter are equal and whose radius is the same as that of the cylindrical secti

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Question 1201164: A rocket consists of a right circular cylinder of height 20 m surmounted by a cone whose height and diameter are equal and whose radius is the same as that of the cylindrical section. What should this radius be (rounded to two decimal places) if the total volume is to be
700𝜋/3
m^3?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let r be the radius of the cylinder, and therefore the radius of the cone also.

Since the height of the cone is the diameter of the cone, the height of the cone is 2r.

The volume of the cylinder is V=%28pi%29%28r%5E2%29%28h%29=20%28pi%29%28r%5E2%29

The volume of the cone is V=%281%2F3%29%28pi%29%28r%5E2%29%28h%29=%281%2F3%29%28pi%29%282r%5E3%29

The total volume is the sum of the volumes of the cylinder and cone.

As suggested by the instruction to round the answer to 2 decimal places, the answer is some ugly irrational number -- use a calculator to find the radius for which the total volume is 700𝜋/3.