A storage container is in d form of a frustum of a right pyramid 4m square at d top and 2.5m square at d bottom. If d container is 3m deep, what is its capacity in m3?
I want d answ
Proper English please , "d form" is not English.
Looks at the fulcrum as a pyramid with its top cut off.
Let the height of the missing piece be h m
then:
h/(h+3) = 2.5/4
4h = 2.5h + 7.5
1.5 h = 7.5
h = 5 <----- the height of the imaginary pyramid that was cut off.
volume of a pyramid = (1/3)(area of base)(height)
volume of the "whole" pyramid = (1/3)(4)(8) = 32/3 m^3
volume of the pyramid that was cut off = (1/3)(2.5)(5) = ..... m^3
volume of the fulcrum = whole pyramid - cut-off pyramid
= .....
Well, let's calculate the capacity of this frustum-shaped storage container. To do that, we need to find the volume of this pyramid-shaped container.
The formula for the volume of a frustum of a pyramid is:
V = (1/3)h (A₁ + A₂ + √(A₁A₂))
Where:
V = volume
h = height
A₁ = area of the top base
A₂ = area of the bottom base
So, plugging in the values given:
V = (1/3) * 3m * (4m² + 2.5m² + √(4m² * 2.5m² ))
Calculating this:
V = (1/3) * 3m * (4m² + 2.5m² + √(10m⁴))
V = m³ * (10m² + √(10m⁴))
Now, I'm no math wizard, but it seems that further simplification isn't possible given the information provided. Therefore, the capacity of this frustum-shaped storage container is approximately m³ * (10m² + √(10m⁴)).
To find the capacity of the storage container, we first need to find its volume.
The volume of a frustum of a pyramid can be calculated using the formula:
V = (1/3)h (A1 + A2 + √(A1 * A2))
Where:
V = Volume of frustum
h = Height of frustum
A1 = Area of the top base
A2 = Area of the bottom base
Given:
A1 = 4m² (area of the top base)
A2 = 2.5m² (area of the bottom base)
h = 3m (height of the frustum)
Substituting the given values into the formula, we have:
V = (1/3)(3)(4 + 2.5 + √(4 * 2.5))
Simplifying the equation, we get:
V = (1/3)(3)(6.5 + √(10))
V = (1)(6.5 + √(10))
V = 6.5 + √(10)
Therefore, the capacity of the storage container is approximately 6.5 + √(10) cubic meters.
To find the capacity of a frustum of a pyramid, we need to calculate the volume of the larger pyramid and the smaller pyramid, and then subtract the smaller volume from the larger volume.
First, let's calculate the volume of the larger pyramid:
The formula to calculate the volume of a pyramid is: (1/3) * base area * height
In this case, the base area of the larger pyramid is 4 meters squared and the height is 3 meters.
Volume of the larger pyramid = (1/3) * 4 * 3 = 4 cubic meters
Now, let's calculate the volume of the smaller pyramid:
The base area of the smaller pyramid is 2.5 meters squared and the height is also 3 meters.
Volume of the smaller pyramid = (1/3) * 2.5 * 3 = 2.5 cubic meters
Finally, to find the capacity of the storage container, we subtract the volume of the smaller pyramid from the volume of the larger pyramid:
Capacity = Volume of the larger pyramid - Volume of the smaller pyramid
= 4 cubic meters - 2.5 cubic meters
= 1.5 cubic meters
Therefore, the capacity of the storage container is 1.5 cubic meters.