Calculating the Volume of a 6-Sided Box

[thereddevils]

Homework Statement

The diagram shows a box that has six faces .The top and bottom faces are square . THe other faces are all identical. What is the volume of the box ?

Homework Equations

The Attempt at a Solution

 

[Axiom17]

What's your attempt so far? I.e. method and calculations?

 

[njama]

Hint: It is Pyramidal Frustum. Correct me if I am wrong.

 

[Axiom17]

Hint: It is Pyramidal Frustum. Correct me if I am wrong.

No that's what I was thinking too cheers njama on posting the link

OK, so thereddevils give that a go now!

 

[thereddevils]

No that's what I was thinking too cheers njama on posting the link

OK, so thereddevils give that a go now!

ok so from the formula for volume of a pyramidal frustum is given by

V=1/3(A1 + A2 + root(A1)(A2))(h)

the height is root(18)

A1=100 , A2=16

i got V=220 cm^3

but the answer given is 312 cm^3.

 

[rl.bhat]

According to the diagram h = 6 cm.

 

[Axiom17]

Yes the formula is:

$$V=\frac{1}{3}h \left( A_{1}+A_{2}+\sqrt{A_{1}\times A_{2}} \right)$$

Where $A_{1}$ is the bottom area, $A_{2}$ is the top area, and $h$ is the height. Refer to your diagram for these values.

If you check that you're using all of the correct values , then you'll get the answer.