A storage container is in form of a frustum of a pyramid form a square at the top or and 2.5 mm square at the bottom if the container is 3 m deep what is this capacity in metre cube
To find the volume of the frustum, we need to use the formula:
V = (1/3)h(A₁ + A₂ + √(A₁A₂))
where:
V = volume of frustum
h = height of frustum
A₁ = area of top square
A₂ = area of bottom square
Given:
- A₁ = 2.5 mm²
- A₂ = 3² = 9 m²
- h = 3 m
We need to convert A₁ to m²:
A₁ = 2.5 mm² = (2.5/1000)² m² = 6.25 x 10^-7 m²
Substituting the values to the formula:
V = (1/3)(3)[6.25 x 10^-7 + 9 + √(6.25 x 10^-7 x 9)]
V = (1/3)(3)[6.25 x 10^-7 + 9 + √(5.625 x 10^-6)]
V = 3.000002344 m³ (rounded to 9 decimal places)
Therefore, the capacity of the storage container is approximately 3.000002344 m³.
To find the capacity of the storage container, we need to calculate the volume of the frustum of the pyramid.
The frustum of a pyramid formula is:
V = (1/3)πh(b1^2 + b2^2 + b1 * b2)
Where:
V = Volume
h = Height
b1, b2 = Area of the top and bottom bases of the frustum
Given:
Height (h) = 3 m
Square at the top (b1) = 2.5 mm square (or 2.5 * 10^-3 m)
Square at the bottom (b2) = 2.5 mm square (or 2.5 * 10^-3 m)
Converting the dimensions to meters, we have:
b1 = 2.5 * 10^-3 m
b2 = 2.5 * 10^-3 m
Now, we can calculate the volume of the frustum:
V = (1/3)πh(b1^2 + b2^2 + b1 * b2)
= (1/3) * 3.14 * 3 * ((2.5 * 10^-3)^2 + (2.5 * 10^-3)^2 + (2.5 * 10^-3) * (2.5 * 10^-3))
= (1/3) * 3.14 * 3 * (6.25 * 10^-6 + 6.25 * 10^-6 + 6.25 * 10^-6)
= (1/3) * 3.14 * 3 * 18.75 * 10^-6
= 0.0626 m^3
Therefore, the capacity of the storage container is approximately 0.0626 cubic meters.
To find the capacity of the storage container, we need to calculate the volume of the frustum pyramid.
The formula for the volume of a frustum pyramid is given by:
V = (1/3) * h * (A + sqrt(A * B) + B)
Where:
V is the volume of the frustum pyramid
h is the height
A is the area of the top square
B is the area of the bottom square
In this case, the height of the container is 3 m.
First, we need to calculate the areas of the top and bottom squares:
A = (2.5 mm)^2 (Convert from mm to meters: 1 m = 1000 mm)
A = (2.5 * 10^(-3))^2
A = 6.25 * 10^(-6) m^2
B = (2 * 2.5 mm)^2 (Convert from mm to meters: 1 m = 1000 mm)
B = (5 * 10^(-3))^2
B = 2.5 * 10^(-5) m^2
Now we can substitute the values into the formula:
V = (1/3) * 3 m * (6.25 * 10^(-6) m^2 + sqrt(6.25 * 10^(-6) m^2 * 2.5 * 10^(-5) m^2) + 2.5 * 10^(-5) m^2)
Calculating the values inside the square root:
sqrt(6.25 * 10^(-6) m^2 * 2.5 * 10^(-5) m^2) = sqrt(15.625 * 10^(-11) m^4)
sqrt(15.625 * 10^(-11) m^4) = 3.952 m^2 * 10^(-6) m^2
Now we can substitute the values back into the formula:
V = (1/3) * 3 m * (6.25 * 10^(-6) m^2 + 3.952 m^2 * 10^(-6) m^2 + 2.5 * 10^(-5) m^2)
Simplifying the equation:
V = (1/3) * 3 m * (10.202 * 10^(-6) m^2)
V = 10.202 * 10^(-6) m^3
Therefore, the capacity of the storage container is 10.202 * 10^(-6) m^3 or approximately 0.000010202 m^3.