Math Is Fun Forum

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Help on Cylinder Volume Problem

A right cylindrical oil tank is 15 feet tall and its circular bases have diameters of 4 feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is 3 feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? Express your answer as a decimal to the nearest tenth.

Could you help me solve this problem? Thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Help on Cylinder Volume Problem

hi dazzle1230

Here's a view of the cylinder on its side.  The coloured region shows the oil.

You know enough measurements to calculate the angle ACB and hence the area of the sector from A through D to B (angle/360 times pi r^2).  Also the area of the triangle ABC.  Hence the area of the coloured segment.

So this will allow you to calculate the volume of oil.  When the cylinder is upright that volume will be h times pi r^2 where h is the required height.

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help on Cylinder Volume Problem

Possibly AB is above C.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Help on Cylinder Volume Problem

Thanks thickhead.  In my mind I  had the radius as 4 not the diameter.  I have amended my diagram.  Method is essentially the same.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: Help on Cylinder Volume Problem

I got it.  Thank you so much for the help!