Monica is constructing a box in the shape of a right rectangular prism to hold grain on her farm. Use the formula for the volume of a rectangular prism to find the area of the base when the volume is 50 ft.³ and the height is 4 feet.
The formula for the volume of a rectangular prism is given by:
Volume = length × width × height
In this case, we are given the volume (50 ft³) and the height (4 feet). Let's assume the length is 'l' and the width is 'w', so we have:
50 ft³ = l × w × 4 feet
To find the area of the base, we need to solve for either the length or the width to find one of its dimensions. Let's solve for 'l' by rearranging the equation:
l = 50 ft³ / (w × 4 feet)
Now, we can substitute this expression for 'l' into the area formula for a rectangle:
Area of the base = length × width = (50 ft³ / (w × 4 feet)) × width
Therefore, the area of the base is given by (50w ft³) / 4 feet, which simplifies to:
Area of the base = 12.5w ft²
In conclusion, the area of the base of the right rectangular prism is 12.5w ft², where 'w' is the width of the box.