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

Answer 1

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.