What is the volume of water in an inverted square pyramid with given dimensions?

In summary, the inverted square pyramid has a height of 8m and a top edge of 3m. Its volume is 24m^3 and the initial volume of water in the tank is 3m^3. The formula for volume of a pyramid is 1/3bh, where b is the area of the base. The maximum volume of the pyramid is 24m^3 and the top base, when the water is filled to a depth of 5m, is 1.8m.
  • #1
macmac410
9
0

Homework Statement



An inverted square pyramid has a height equal to 8m and a top edge equal to 3m. Initially, it contains water to a depth of 5m. What is the initial volume of water in the tank?


Homework Equations


volume=1/3bh

where b is e2, as area of square base.



The Attempt at a Solution


the height is given and the sides of square so can easily compute for the volume of the entire pyramid which is
vp(volume of pyramid)=24
the problem is i don't know the next step to get the volume of the liquid.
I tried so many formulas but theses none of those would fit in. HELP!
 
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  • #2
8 times 3 times 1/3 is 24
24/height= changebase or something like that
24m^3/5m=4.8meters-3meters=base=1.8meters is new base when its 5 full
bh1/3=volume
1.8 times 5 times 1/3 is 3meters^3
3 meters cubed should be your answer.
is it? I am no expert though
 
  • #3
I think it is not.
man, I'm really confused..
But anyway thanks for the help.
I need the volume of the water in the pyramid.
 
  • #4
well the maximum volume contained in the pyramid is 8 meter cubed. so, 1.8 meters being the top baes where 5 meters is the height and where the volume is 3 meters cubed when the water is filled 5 meters high makes perfect sense to me.
 
  • #5
No, the maximum volume of the pyramid is 24m^3
since
volume of pyramid is 1/3 bh
where b is the area of bAse..
 
  • #6
b=8
h=3
1/3=constant
8 times 3 times 1/3 is 8 meters cubed
 

What is the formula for finding the volume of an inverted pyramid?

The formula for calculating the volume of an inverted pyramid is V = (1/3) * b * h, where b is the area of the base and h is the height of the pyramid.

How do you measure the base of an inverted pyramid?

The base of an inverted pyramid can be measured using any unit of length, such as centimeters, inches, or feet. The length and width of the base should be measured at its widest points.

Can the volume of an inverted pyramid be negative?

No, the volume of an inverted pyramid cannot be negative. Volume is a measure of the amount of space occupied by an object and cannot have a negative value.

What is the difference between an inverted pyramid and a regular pyramid?

An inverted pyramid has its apex pointing downwards and its base at the top, while a regular pyramid has its apex pointing upwards and its base at the bottom.

Why is the volume of an inverted pyramid useful in real life?

The volume of an inverted pyramid can be used to calculate the capacity of objects with a shape similar to an inverted pyramid, such as storage tanks or buildings with slanted roofs. It is also used in architecture and engineering to determine the necessary materials for construction.

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