A rectangular box with a square base contains 24 cubic feet. if the height of the box is 18 inches, how many feet ae there in each side of the base?
a. 4
b. 2
c. (2 square root of 3)/3
d. square root of 3 / 2
e. square root of 3
V = Lwh
the volume (given) = 24 ft^3
the height (given) = 18" = 1.5'
24 = L*w*1.5
divide both sides by 1.5
16 = Lw
You need to find the number of feet in each side of the base
since the box has a square base
L = W
AND, found above, L*w = 16
which of the above answers, a, b, c or d, when multiplied by itself, equals 16?
In simple terms, the answer is A, using what helper said, when you multiply 4 by 4 it equals 16.
To find the length of each side of the base, we need to use the given information to set up an equation.
Since the box has a square base, let's say each side of the base has a length of x feet.
We know that the volume of the rectangular box is 24 cubic feet.
The volume of a rectangular box is given by the formula: Volume = Length x Width x Height.
In this case, the volume is 24 cubic feet, the height is 18 inches (which is equal to 1.5 feet), and the sides of the base have a length of x.
So, the equation becomes: 24 = x * x * 1.5
Simplifying the equation: 24 = 1.5x^2
Divide both sides of the equation by 1.5: 16 = x^2
Take the square root of both sides: √16 = √(x^2)
Simplifying: 4 = x
Therefore, the length of each side of the base is 4 feet.
Hence, the correct answer is option a. 4.
To find the length of each side of the base of the rectangular box, we need to use the given information.
First, we convert the height of the box from inches to feet. Since there are 12 inches in a foot, dividing 18 inches by 12 gives us:
Height in feet = 18 inches / 12 = 1.5 feet
Let's denote the length of each side of the base as x.
Since the box has a square base, the volume of the rectangular box can be calculated as:
Volume = Length of base * Length of base * Height
Given that the volume is 24 cubic feet and the height is 1.5 feet, we can substitute these values into the equation:
24 = x * x * 1.5
Now, let's solve for x:
24 = 1.5x^2
Divide both sides of the equation by 1.5:
16 = x^2
Taking the square root of both sides, we get:
√16 = √(x^2)
4 = x
Therefore, each side of the base of the rectangular box is 4 feet.
The correct answer is a. 4.