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
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
5 answers
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
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?
Hmmmmmmmmm.....
A little bit helpful
1 answer