Question

find the volume of frustum of a regular square pyramid if the base edges are 14 cm and 38 cm, and the measure of one of its lateral edges is 24 cm.

Answer 1

visualize a frustum of a regular square pyramid. the volume can be expressed as the difference of the volumes of two pyramids: the pyramid with the larger base minus the pyramid with the smaller base that has been cut off.

Answer 2

Are a of a square-based pyramid is\[\frac{ 1 }{ 3 } side^2 \times height\]

Answer 3

well i use the apothem formula or simply squaring the base edges, is it the right thing to do?

Answer 4

I don't know the apothem formula for three-dimensional figures

Answer 5

i just use the apothem formula of polygons, is it right?

Answer 6

they tell you it is square-based, just square the side.
you have all the information you need to finish the problem.

Answer 7

yes, if you used the apothem formula it would be right.

Answer 8

ok so should i consider the lateral edge which is 24 cm to be the slant height of the frustum? so that i can use it to find the altitude by Pythagorean formula

Answer 9

for the way to solve the problem that I know, you want the height of the imaginary pyramid A and the height of the imaginary pyramid B. There probably is a way to find the volume with the height of the frustum, but I don't know exactly how to do that.

Answer 10

yes, then how should i use the formula you gave if i don't have the height?

Answer 11

set up a triangle to represent one side of the imaginary pyramid A.

Answer 12

ok thats what i did and my final answer is way to far to right one, by the way the formula i am using is\[V = 1/3h(B1+B2+\sqrt{BIB2}\] is this right?

Answer 13

where B1 is the area of bigger measure and B2 is the area of the smaller one

Answer 14

where does that formula come from?

Answer 15

it came from the book

Answer 16

so what did you use for h?

Answer 17

the one i get by doing the pythagorean formula which is \[12\sqrt{3}\] from \[h=\sqrt{(24^2)-(19-7)^2}\]
is it right?

Answer 18

http://mathworld.wolfram.com/PyramidalFrustum.html also you can find it here