Susan is going to build some large wooden storage boxes. The boxes are shaped like rectangular prisms, as shown below. She wants to cover all the sides of each box with special wallpaper. If she has a total of 1328 ft of wallpaper, how many boxes can she cover?
(Angles are 4ft, 7ft, and 5ft)
Sky is going to build some large wooden storage boxes. The boxes are shaped like a rectangular prism with the width of 7 feet, length of 9 feet and height of 8 feet. She wants to cover all the sides of each box with special wallpaper. If she has a total of 1,910 square feet of wallpaper, how many boxes can she cover?
To calculate the total amount of wallpaper needed to cover a box, we need to find the surface area of the box.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given the dimensions of the box:
Length (l) = 4 ft
Height (h) = 7 ft
Width (w) = 5 ft
Substituting these values into the formula:
Surface Area = 2(4)(7) + 2(4)(5) + 2(7)(5)
Surface Area = 56 + 40 + 70
Surface Area = 166 ft^2
Therefore, each box requires 166 square feet of wallpaper to cover.
To find out how many boxes Susan can cover with the given amount of wallpaper (1328 ft), we can divide the total amount of wallpaper by the wallpaper required for each box:
Number of boxes = Total wallpaper / Wallpaper required for each box
Number of boxes = 1328 ft^2 / 166 ft^2
Number of boxes = 8
Susan can cover 8 boxes with a total of 1328 ft of wallpaper.
To determine the number of boxes Susan can cover, we first need to find the total surface area of each box.
A rectangular prism has six faces, and to cover all the sides, we need to find the total surface area. The formula to calculate surface area for a rectangular prism is:
Surface Area = 2 * (length * width + length * height + width * height)
Let's substitute the values given in the question:
Surface Area = 2 * (4ft * 7ft + 4ft * 5ft + 7ft * 5ft)
Simplifying this equation, we get:
Surface Area = 2 * (28ft² + 20ft² + 35ft²)
Surface Area = 2 * 83ft²
Surface Area = 166ft²
Each box has a surface area of 166 square feet.
Given that Susan has a total of 1328 ft of wallpaper, we can divide this value by the surface area of each box to determine how many boxes she can cover:
Number of Boxes = Total wallpaper / Surface Area of each box
Number of Boxes = 1328ft² / 166ft²
Dividing 1328 by 166, we get:
Number of Boxes ≈ 8
Therefore, Susan can cover approximately 8 boxes with the given wallpaper.