A square based pyramid, with a perpendicular height of 15cm I'd placed on a table.
The weight of the pyramid is 70.56N. The pyramid exerts a pressure of 4900N/m^2 on the table.
Work out the volume of the square based pyramid.
Thank you so much.
To find the base area,
70.56N / (4900N/m^2) = 0.0144 m^2 = 144cm^2
v = 1/3 * 144 * 15 = 720 cm^3
Why did the square-based pyramid go to the gym? To get in shape and exert some pressure on the table, of course!
But let's get back to your question. To find the volume of the pyramid, we need to use its formula:
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a square, so the formula becomes:
Volume = (1/3) * side length * side length * height
Now, we know the perpendicular height is 15 cm, and the pressure exerted by the pyramid on the table is 4900 N/m^2. We can use this information to find the base area:
Pressure = Force / Area
Rearranging the formula for area, we get:
Area = Force / Pressure
Substituting the values, we have:
Area = 70.56 N / 4900 N/m^2
Now, since we have the area, we can solve for the side length of the square base:
Area = side length * side length
substituting the values, we have:
side length * side length = 70.56 N / 4900 N/m^2
Now, solving for the side length, we get:
side length = √(70.56 N / 4900 N/m^2)
Using the side length and height, we can now calculate the volume:
Volume = (1/3) * (√(70.56 N / 4900 N/m^2))^2 * 15 cm
Once you simplify the equation, you will have the volume of the pyramid.
To calculate the volume of a square based pyramid, you need to know the base area and the height of the pyramid. The formula for the volume of a pyramid is:
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a square. Let's assume the length of one side of the square base is "x".
To find the base area, you can square the length of one side of the square base:
Base area = x^2
We are also given the perpendicular height of the pyramid, which is 15 cm.
Now, we can substitute the known values into the formula for volume:
Volume = (1/3) * x^2 * 15
However, we currently don't have the value of "x" or the length of one side of the square base. So we need to find it.
Given that the pyramid exerts a pressure of 4900 N/m^2 on the table, we can use this information to find the value of "x".
Pressure = Force / Area
The pressure on the table is given as 4900 N/m^2, and the weight of the pyramid is 70.56 N. Since the base of the pyramid is a square, we can assume the area of the base is x^2.
Substituting the values into the formula, we get:
4900 N/m^2 = 70.56 N / x^2
To isolate "x" in this equation, we can rearrange it:
x^2 = 70.56 N / 4900 N/m^2
Simplifying the equation:
x^2 = 0.0144 m^2
Taking the square root of both sides, we find:
x = sqrt(0.0144 m^2)
x ≈ 0.12 m
Now that we have the value of "x," we can substitute it back into the formula for volume:
Volume = (1/3) * (0.12 m)^2 * 15 cm
However, we need to make sure the units are consistent. Since the height was given in centimeters and the base length was converted to meters, let's convert the height to meters as well:
15 cm = 0.15 m
Now, the formula for volume becomes:
Volume = (1/3) * (0.12 m)^2 * 0.15 m
Calculating the volume:
Volume = (1/3) * 0.0144 m^3 * 0.15 m
Volume ≈ 0.000864 m^3
Therefore, the volume of the square based pyramid is approximately 0.000864 cubic meters.
To find the volume of a pyramid, you can use the formula:
Volume = (1/3) * base area * height
In this case, the base of the square pyramid is a square. Let's assume each side of the square base is denoted by 's'.
Since the square base of the pyramid has equal sides, the area of the base can be calculated by simply squaring the length of one side:
Base Area = s^2
The height of the pyramid is given as 15cm.
Now, let's first calculate the length of one side of the square base. To do this, we can make use of the given information about the pressure exerted by the pyramid on the table.
Pressure = Force / Area
In this case, the pressure exerted by the pyramid on the table is given as 4900 N/m^2. The area upon which the pyramid is exerting pressure is the base area of the pyramid, which is s^2.
Plugging in the values:
4900 N/m^2 = 70.56 N / (s^2)
To solve for s^2, we can rearrange the equation:
s^2 = (70.56 N) / (4900 N/m^2)
s^2 = 0.0144 m^2
Now, we can find the value of s:
s = sqrt(0.0144 m^2)
s ≈ 0.12 m
Now that we know the length of one side of the square base, we can calculate the volume of the pyramid:
Volume = (1/3) * base area * height
Volume = (1/3) * (0.12 m)^2 * 0.15 m
Volume ≈ 0.00216 m^3
Therefore, the volume of the square-based pyramid is approximately 0.00216 cubic meters.