Question
A frustum of a pyramid is 16 cm square at the bottom ,6 cm square at the top ,and 12 cm high.Find the volume of the frustum
Answers
oobleck
Consider the whole pyramid, before the top (with height h) was cut off to make the frustrum. Using similar triangles, the missing height is 36/5. So, the volume of the frustrum is
1/3 * 16^2 * (12 + 36/5) - 1/3 * 6^2 * 36/5 = 1552 cm^3
1/3 * 16^2 * (12 + 36/5) - 1/3 * 6^2 * 36/5 = 1552 cm^3
Reiny
make a sketch to show the complete pyramid
edge of bottom = 4
edge of top of frustum = √6
height of imagined missing pyramid --- h
by ratios:
h/(h+4) = √6/4
4h = √6h + 4√6
h = 4√6/(4 + √6)
Volume of complete pyramid = (1/3)(16)(4√6/(4 + √6)) = ...
Volume of missing pyramid = (1/3)(6)(4√6/(4 + √6)) = ....
volume of frustum = the difference of these two volumes
edge of bottom = 4
edge of top of frustum = √6
height of imagined missing pyramid --- h
by ratios:
h/(h+4) = √6/4
4h = √6h + 4√6
h = 4√6/(4 + √6)
Volume of complete pyramid = (1/3)(16)(4√6/(4 + √6)) = ...
Volume of missing pyramid = (1/3)(6)(4√6/(4 + √6)) = ....
volume of frustum = the difference of these two volumes
Reiny
copy error:
h/(h+4) = √6/4 should have been h/(h+12) = √6/4
followed by the necessary changes.
btw, oobleck interpreted it as a square base with sides 16 cm, whereas I interpreted "16 cm square" to have a base of 16 cm^2
mmmhhh?
h/(h+4) = √6/4 should have been h/(h+12) = √6/4
followed by the necessary changes.
btw, oobleck interpreted it as a square base with sides 16 cm, whereas I interpreted "16 cm square" to have a base of 16 cm^2
mmmhhh?
Nike
Hmmmmmmmmm.....
Stephanie
A little bit helpful