SOLUTION: A right pyramid on a base 4cm square has a slant edge of 6cm. Calcilate the volume of the pyramid. Explain with diagram

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Question 1136492: A right pyramid on a base 4cm square has a slant edge of 6cm. Calcilate the volume of the pyramid. Explain with diagram
Answer by MathLover1(20850) About Me  (Show Source):
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A right pyramid on a base 4cm square has a slant edge of 6cm. Calculate the volume of the pyramid. Explain with diagram

the half of diagonal of the base, a slant edge and height of the pyramid form right triangle where slant edge is hypotenuse, half of diagonal of the base one leg, and height of the pyramid the other leg
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first find diagonal of base:
d%5E2+=+4%5E2+%2B+4%5E2
d%5E2+=+32
d=+sqrt%2832%29
d+=+4sqrt%282%29

then h%5E2=6%5E2+%2B+%282sqrt%282%29%29%5E2
h%5E2+=+36-8
h%5E2+=+28
h+=+sqrt%2828%29
h+=+2sqrt%287%29

and volume is: %281%2F3%29*Area of the base * Height
Area of the base: b=4cm%2A4cm=16cm%5E2


V=+%281%2F3%29+b%2Ah
V=+%281%2F3%29%2816cm%5E2%29%2A2sqrt%287%29cm
V=+%2832%2F3%29sqrt%287%29cm%5E3+ or approximately 28.22cm%5E3