a square pyramid resting on its base is filled to half its height with 320 cm^3 water. how much water is needed to finish filling the pyramid?

I misread the problem. I was thinking the original volume was 320.

Instead, 320 is 7/8 of the original volume, so we still need 1/8 of the original volume to finish filling it. That is 1/7 of what was already used, or 320/7 = 45.7 cm^3

at half its height, all linear dimensions are also half their original values.

So, the base of the empty pyramid is 1/4 the base of the whole pyramid.

empty volume is thus (B/4)*(h/2) = Bh/8 = 40

To solve this problem, we need to calculate the volume of the entire square pyramid and then subtract the volume that is currently filled with water.

First, we need to determine the volume of the pyramid. The volume of a square pyramid is given by the formula:

Volume = (1/3) * Base Area * Height

In this case, since the pyramid is resting on its base, the base area is a square. So, we need to calculate the area of one side of the base and then square it.

Next, we'll calculate the height of the pyramid, which is not given in the question. However, since we know it is filled to half its height, we can determine the height based on the amount of water filled.

Let's calculate the volume of the pyramid step by step:

Step 1: Calculate the area of one side of the base
To calculate the area of one side of the base, we need to know the length of one side of the base. Let's assume it is 's'.

Area of one side of the base = s^2

Step 2: Calculate the base area
Since it is a square base pyramid, there are four equal sides. Therefore, the base area is:

Base Area = 4 * (s^2)

Step 3: Calculate the height of the pyramid
The pyramid is filled to half its height with 320 cm^3 water. Let's assume the total height of the pyramid is 'h'. The filled portion will be half of 'h', so:

Half Height = h/2

Step 4: Calculate the volume of the pyramid
Using the formula for the volume of a pyramid:

Volume = (1/3) * Base Area * Height

Volume = (1/3) * [4 * (s^2)] * (h/2)

Step 5: Subtract the filled volume from the total volume
We know that the filled volume is 320 cm^3, so:

Remaining Volume = Total Volume - Filled Volume

Now, let's substitute the values and solve the equation.