Mensuration

Date: 5/16/96 at 23:44:42
From: Anonymous
Subject: Mensuration

1) A car has a rectangular petrol tank, 55cm long, 40cm wide 
and 22 cm deep. If the fuel consumption of the car averages 
8.4L/100km, how far could the car travel with a full tank of 
petrol??
 
I tried finding the volume by going 55 x 40 x 22.
Then I divided 8.4 into the answer but it didn't work.

2) An aquarium took 96 minutes to completely fill with 
water. Water was filling the aquarium at a rate of 25 L 
every 2 minutes. Given that the aquarium was 2m long and 
80cm wide, determine the height of the aquarium.
 
For this question I took 96 divided by 2 x 25 - after that 
I was stuck.

Christopher John Cole

Date: 5/17/96 at 16:38:18
From: Doctor Ken
Subject: Re: Mensuration

Hello!

Here's what's going wrong in the first problem.  Notice that the 
dimensions of the tank are in cm, and the fuel consumption of the car 
is given in liters per 100km.  These don't match!!  You have to make 
them match before you start comparing them to each other.  

When you multiply 55 x 40 x 22, you get the volume of the tank in 
cubic centimeters.  To get the volume of the tank in liters, since 
1 liter is 1000 cubic centimeters (it's the volume of a cube that's 
10 cm on a side), you divide 55 x 40 x 22 by 1000 to get the 
volume in liters.

Then the other thing you should do is convert the fuel consumption to 
a more meaningful figure.  You have 8.4L/100km, which is the same as 
(8.4/100) L/km.  Do that division and you'll have the fuel consumption 
in liters per kilometer.

Your basic method was right, dividing the fuel consumption into the 
volume of the tank, so once you get the units to match up, things 
should go okay.

The next problem is pretty much the same kind of thing - the first 
thing you want to do is get the units to match up and get your 
measures in nice forms. For instance, the aquarium is 2m by 80cm by 
Xcm - how many cubic centimeters is that?  And how many liters?  
Also, if the water goes in at the rate of 25L every 2 minutes, how 
many liters per minute is that?

Good luck!

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/