The areas of the rectangular faces of the box are shown( 90 in.², 60 in.², & 54 in.²). What is the volume of the box?
V = sqrt(90*60*54) = 540 in^3
To find the volume of a rectangular box, you need to multiply the lengths of its three dimensions: length, width, and height. In this case, we are not given the actual dimensions of the box but are provided with the areas of its three rectangular faces.
To find the volume, we need to determine the dimensions of the box. Since we know the areas of the three faces, we can assume that these faces represent the base, the side, and the top of the box.
To find the dimensions, we can use the formula for the area of a rectangle, which is length multiplied by width. Let's assign variables to the dimensions, assuming the length is L, width is W, and height is H.
Given the areas of the three rectangular faces:
Area of the base: LW = 90 in.²
Area of the side: WH = 60 in.²
Area of the top: LH = 54 in.²
Now let's solve this system of equations simultaneously to find the values of L, W, and H:
From the equation LW = 90, we can solve for W:
W = 90 / L
Next, substitute this value in the equation WH = 60:
(90 / L) * H = 60
Finally, substitute this value in the equation LH = 54:
L * (90 / L) = 54
By simplifying and solving these equations, we can find the values of L, W, and H, and consequently, the volume of the box.