he volume of the prism is 3 cubic feet. Find the value of x.
the base is 3''. the height and width is x.
Base * width * height = 3 cubic feet
First convert the base measurement to feet: 3 inches = 1/4 ft
(1/4)*x*x = 3
(1/4)x² = 3
Now solve for x.
16
To find the value of x, we need to set up and solve an equation using the given information.
We know that the volume of the prism is 3 cubic feet. The formula for the volume of a rectangular prism is given by:
Volume = Base Area * Height
The base area of the prism is the product of its length and width. In this case, the length and width are both x.
Base Area = length * width = x * x = x^2
Substituting this into the volume formula, we get:
3 = x^2 * Height
We also know that the base has dimensions of 3'' (inches), which is equivalent to 3/12 = 1/4 feet. Since the base area is x^2, we have:
x^2 = 1/4
To solve for x, we take the square root of both sides:
sqrt(x^2) = sqrt(1/4)
x = 1/2 or -1/2
Since we are dealing with dimensions, only the positive value, x = 1/2, makes sense in this context.
Therefore, the value of x is 1/2.