A storage unit in the shape of a rectangular prism has a volume of 72 ft3. The area of the base of the unit is 18 ft2. What is the volume of a similar unit whose height is 8 ft?
18Ft^2*h1 = 72Ft^3
h1 = 72Ft^3/18Ft^2 = 4 Ft.
A = (8Ft/4Ft) * 18Ft^2 = 36 Ft^2 = Area
of the base.
V = A*h = 36Ft^2 * 8Ft = 288 Ft^3.
Correction:
A =(8/4)^2 * 18 = 72 Ft^2 = Area of the
base.
V = A*h = 72 * 8 = 576 Ft^3.
OR
V = (8/4)^3 * 72Ft^3 = 576 Ft^3.
To find the volume of a similar unit with a height of 8 ft, we need to find the scale factor that relates the two volumes.
The volume of a rectangular prism is given by the formula: Volume = Length × Width × Height.
Let's denote the length of the original storage unit as L, the width as W, and the height as H. We know that the volume (V) of the original unit is 72 ft³, and the area of the base (A) is 18 ft².
Given that the volume (V') of the similar unit with a height of 8 ft, the area of the base (A') will remain the same, i.e., 18 ft².
We can write the following proportions:
V / A = V' / A'
Using the given values, we substitute V = 72 ft³ and A = 18 ft²:
72 / 18 = V' / 18
Simplifying, we get:
4 = V' / 18
Multiplying both sides by 18, we find:
V' = 72 ft³
Therefore, the volume of the similar storage unit with a height of 8 ft is also 72 ft³.
To find the volume of a similar storage unit with a height of 8 ft, we need to determine the new dimensions that maintain the same shape as the original unit.
Given that the area of the base of the original unit is 18 ft^2, and the volume is 72 ft^3, we can determine the height and dimensions of the original unit.
Let's assume the dimensions of the original unit are length (L), width (W), and height (H).
We know that the volume of a rectangular prism is calculated by multiplying the length, width, and height: Volume = L * W * H.
Since the volume of the original unit is 72 ft^3 and the area of its base is 18 ft^2, we can set up an equation:
18 ft^2 * H = 72 ft^3
Dividing both sides of the equation by 18 ft^2, we get:
H = 72 ft^3 / 18 ft^2 = 4 ft
So the height of the original unit is 4 ft.
Now, to find the dimensions of the new unit with a height of 8 ft, we can use the concept of similar shapes. Similar shapes have proportional sides and angles.
Since the height of the similar unit is twice the height of the original unit, we can conclude that all the sides of the new unit are also multiplied by the scaling factor of 2.
Therefore, the length of the similar unit is L * 2, the width is W * 2, and the height is H * 2.
Now, let's find the dimensions of the new unit:
Length of the new unit = L * 2
Width of the new unit = W * 2
Height of the new unit = H * 2 = 8 ft
We know that the volume of the new unit can be calculated as Volume = (Length of new unit) * (Width of new unit) * (Height of new unit).
Substituting the values, we get:
Volume of the new unit = (L * 2) * (W * 2) * 8 ft = 4LW * 8 ft
Since we know the volume of the new unit is the same as the original unit, we can equate the two volumes:
4LW * 8 ft = 72 ft^3
Dividing both sides of the equation by 32, we get:
LW = 72 ft^3 / 32 ft = 2.25 ft^2
Now we need to find the value of LW to calculate the volume of the new unit.
There are multiple values of L and W that can give us LW = 2.25 ft^2, as long as their product equals 2.25 ft^2. For example, L = 1.5 ft and W = 1.5 ft or L = 0.75 ft and W = 3 ft.
Using one of these possible dimensions, we can calculate the volume of the new unit:
Volume of the new unit = 4LW * 8 ft = 4 * 1.5 ft * 1.5 ft * 8 ft = 18 ft^3
Therefore, the volume of a similar storage unit with a height of 8 ft is 18 ft^3.