write and solve an equation to find the missing dimension of the rectangular prism.
Volume= 1km cubic
L=3/4 km
W=2/3 km
H= ?
To find the missing dimension of the rectangular prism, we can use the formula for volume of a rectangular prism:
Volume = length × width × height
In this case, the volume is given as 1 km^3 (cubic kilometer), and the length (L) and width (W) are given as fractions of a kilometer.
First, let's substitute the given values into the formula:
1 km^3 = (3/4) km × (2/3) km × H
Next, let's simplify the equation:
1 km^3 = (1/2) km^2 × H
Now, let's isolate H by dividing both sides of the equation by (1/2) km^2:
(1 km^3) ÷ (1/2) km^2 = H
Since dividing by a fraction is the same as multiplying by its reciprocal, we can rewrite the equation as:
(1 km^3) × (2/1 km^2) = H
Simplifying the right side of the equation gives:
(2 km^3) / (1 km^2) = H
Finally, performing the division gives us the solution:
H = 2 km
Therefore, the missing dimension of the rectangular prism is H = 2 km.