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December 21, 2014

December 21, 2014

Posted by **m** on Wednesday, January 5, 2011 at 9:52am.

I am confused on how to do surface area and volume if V=1/3bh and we don't know the height? Same with trying to figure out the surface area?

- math -
**Damon**, Wednesday, January 5, 2011 at 10:16amI suspect you are missing something in the problem statement but

the base seems to be square, 2 by 2 so the base area = 4

then the volume v is 1/3 *the area of the base * the height

v = (1/3)4 h

I assume the surface area you mean is the area of the sides, not including the base.

Look at one of the sloping sides. Its base is 2 but we need to find its altitude by using trig. It is the hypotenuse of a triangle whose base is 1 and height is h

therefore the altitude is sqrt(1+h^2)

therefore the area of one side is

(1/2)(2)(sqrt(1+h^2))

and the total area of all four sides is

4 sqrt(1+h^2)

so v = 4/3 h

the minimum is of course when h = 0

a = 4 (1+h^2)^.5

da/dh = 4(.5)(1+h^2)^-.5 * 2h

this is clearly zero when h = 0

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