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Macy

Guest

Calculate volume

Please help me to work out the following questions:

1. The interior of drinking glass is a cylinder of diameter 8cm and height 12 cm. The glass is held at an angle 45 degree from the vertical and filled until the base is just covered. How much water, in mm , is in the glass?

2. PQR is an equilateral triangle. The point U is the midpoint of PR. Points T and S divide QP and QR in the ratio 1:2. The point of intersection of PS, RT and QU is X. If the area of triangle QSX is 1 square units, what is the area, in square units of equilateral triangle PQR?

Thank in advance
Macy

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Calculate volume

#1.)
Answer: 64pi cc's and a cc is a ml (milliliter).
a cubic cm is a cc or a ml.
a cylinder cut diagonally is 1/2 the volume.
area of base = 4times4timesPI = halfDiameterTimesHalfDiameterTimesPi
Multiply area of base (16pi) in cm, by
half the height of water (8/2).  The water is
8 cm up the side since a 45deg angle makes both base and side the same.
So 4 times 16pi is volume of water, or 64pi in cm^3, or milliliters, or cc's, cubic centimeters.
If you want it in cubic millimeters, then multiply by 10 three times.
64pi times 10 times 10 times 10 would be 64000pi cubic millimeters.

Last edited by John E. Franklin (2008-08-07 16:05:52)

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Calculate volume

#2.)  point X is exactly halfway between Q and U.
I didn't finish area yet...

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igloo myrtilles fourmis

Macy

Guest

Re: Calculate volume

Thank you, John. i did not realise the shape change