Pam W.

asked • 05/31/14# identify given and unknown info

top of refrig has an area of .06m2 Height of frig is 180cm What volume does it occupy in cubic meters. identify given and unknown info. show formuls. what is unknown variable?

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## 1 Expert Answer

Caleb M. answered • 05/31/14

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Mathematics Tutor

Knowns:

Well, we know the cross sectional area of the fridge (the area of a slice of the fridge. Here this is the area of the top of the fridge. Since we will assume this fridge has the same shape, say rectangular, if you cut the fridge into two pieces the area of a 'slice' at that point would have the same cross sectional area), and we know the height of the fridge.

Unknown: The volume of the fridge.

Approach: In an object in 3-dimensions has the same cross sectional shape and area then it's volume is given by

V= B*h

where B is the area of a 'slice' and h is the height. What does this mean? This is easiest to see with examples. Imagine a cube, if I cut the cube horizontally I and look at my cut from above, I see a square. No matter where I cut, I get a square of the same area. This means that the volume of the cube is

V= B*h=s^2 * s=s^3

Since B=s^2 (the area of the square) and h=s (because a cube has sides of all the same length)

This confirms the formula you should be familiar with.

A giant rectangular box has this same property. However, a ball would not. Each slice would have the same shape - a circle - but not the same area.

Now back to the problem! We know the fridge has the same shape everywhere with the same area. So as we said,

V= B*h

But B=0.06 m^2 and h=180cm. We need to be careful here! Our units need to be the same otherwise it's like working with apples and oranges! h=180cm=1.8 m. Then

V = B*h = 0.06 m^2 * 1.8 m = 0.108 m^3

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Ebenezer O.

05/31/14