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 cubic feet and the height is 4 feet.(1 point)
Responses
6.25 ft.2
6.25 feet squared
37.5 ft.2
37.5 feet squared
200 ft.2
200 feet squared
12.5 ft.2
To find the area of the base of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:
Volume = length x width x height
In this case, the volume is given as 50 cubic feet and the height is 4 feet. We can rearrange the formula to solve for the area of the base:
Area of base = Volume / (height x width)
Plugging in the given values:
Area of base = 50 cubic feet / (4 feet x width)
To solve for the width, we can divide both sides of the equation by 4 feet:
Area of base / 4 feet = 50 cubic feet / (4 feet x width)
Simplifying:
Area of base / 4 feet = 12.5 cubic feet / width
Now, we can solve for the width by multiplying both sides of the equation by width:
(width x Area of base) / 4 feet = 12.5 cubic feet
Multiplying both sides of the equation by 4 feet:
width x Area of base = 50 cubic feet
Since the area of the base is the unknown, let's represent it with the variable A. The equation becomes:
width x A = 50 cubic feet
Now, we need to solve for A. We can do this by dividing both sides of the equation by the width:
A = 50 cubic feet / width
Therefore, the area of the base is 50 cubic feet divided by the width.
Given that the height is 4 feet, we have the following answer choices:
6.25 ft.2
6.25 feet squared
37.5 ft.2
37.5 feet squared
200 ft.2
200 feet squared
12.5 ft.2
None of these answer choices is correct because the area of the base depends on the width. Without knowing the width, we cannot determine the exact area of the base.