Tuesday, April 18, 2006

Surface Area & Volume Questions`

Problem 2 (harder) 2. Mr. Bloop has a cylindrical water tank on his farm. It is three metres long and 60 centimetres in diameter. Water flows out a valve in the bottom of the tank at a rate of 0.8 cubic metres per second. How long will it take the tank to empty?

Well, there are 100 cm in a metre. To start off, you find the volume of the cylinder by finding the circumfrence. You mulitply 3.14 by 60 which gives you 188.4.

Then you multiply that by 300 centimetres which will give you 56520. Since it leaks 0.8 cubic metres every second. Well, it leaks 48 cubic metres a minute (60 x 0.8). Since there is 60 minutes in an hour I multiplied 60 by 48 to get 2880.

The tank leaks 2880 cubic metres every hour. So I subtracted 2880 from 56520 to get 53640. Then you keep subtracting until you get down to zero.
After long CALCULATOR work. It takes 19 hours, 37 minutes and 19 seconds for the tank to become empty. I think that is right.

Problem 3 (easy) 3. If you have five 5 cm by 5 cm x 5 cm aluminum cubes and superglue them together in a row, what is the surface area of the resulting shape made by the five cubes?

You start off by finding the surface area for each cube. There are six sides and each side is 25 cm2. You multiply 25 by 6 to get 150. Since the sides are going to be glued you are going to have to be aware that some sides don't count in the total meaurement. The three cubes in the middle are each 100 cm2 cause TWO sides of the cubes are not included. The end cubes are 125 cm2 cause each cube has ONE side not included.

Add up the total areas : 125 + 100 + 100 + 100 + 125 = 550 cm2
Total surface area of the cube chain is 550 cm2
Blah.. Hope they are right

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