URGENT HELP PLEASE!
find the surface area and volume of the following possible cereal boxes determine the cost of making the box assuming the cardboard costs 5 cents per square inch
box 1 rectangle: 12 inch in height 7.5 inches wide 2 inches thick
Box 2 is a pyrmid that is 12in tall 8 inches wide on the botton on one side and the other side 12.6 inches tall and 6inch on the bottom
Box 3 is a cylinder shape and the top is2.5 inches wide and height is 12inch PLEASE GIVE ACCURATE ANSWER AND YES THIS IS THE UNIT 5 PORTIFILLO IN CONNEXUS
I'm on the same thing right now I cant figure it out:/
Someone? : \
To find the surface area and volume of each cereal box, you need to use the formulas specific to each shape.
Box 1: Rectangle
The surface area of a rectangular box can be found by adding the areas of all six faces.
- The front and back faces have dimensions 12 inches (height) by 7.5 inches (width) = 12 * 7.5 = 90 square inches each.
- The top and bottom faces have dimensions 7.5 inches (width) by 2 inches (thickness) = 7.5 * 2 = 15 square inches each.
- The two side faces have dimensions 12 inches (height) by 2 inches (thickness) = 12 * 2 = 24 square inches each.
Therefore, the total surface area of Box 1 is the sum of all face areas: 90 + 90 + 15 + 15 + 24 + 24 = 258 square inches.
The volume of a rectangular box is found by multiplying the three dimensions together.
- The volume of Box 1 is 12 inches (height) * 7.5 inches (width) * 2 inches (thickness) = 180 cubic inches.
To determine the cost of making the box, assuming the cardboard costs 5 cents per square inch, multiply the surface area by the cost per square inch.
- The cost of making Box 1 would be 258 square inches * $0.05/square inch = $12.90.
Box 2: Pyramid
The surface area of a pyramid can be found by adding the areas of the base and the four triangular faces.
- The base of the pyramid has dimensions 8 inches (width) by 6 inches (length) = 8 * 6 = 48 square inches.
- The two triangular faces adjacent to the shorter base have dimensions 8 inches (width) by 12 inches (height) / 2 = 48 square inches each.
- The two triangular faces adjacent to the longer base have dimensions 12.6 inches (height) by 6 inches (width) / 2 = 37.8 square inches each.
Therefore, the total surface area of Box 2 is the sum of all face areas: 48 + 48 + 37.8 + 37.8 = 171.6 square inches.
The volume of a pyramid is found by multiplying the area of the base by the height and then dividing by 3.
- The volume of Box 2 is 48 square inches (base area) * 12 inches (height) / 3 = 192 cubic inches.
To determine the cost of making the box, assuming the cardboard costs 5 cents per square inch, multiply the surface area by the cost per square inch.
- The cost of making Box 2 would be 171.6 square inches * $0.05/square inch = $8.58.
Box 3: Cylinder
The surface area of a cylinder is the sum of the areas of its two circular bases and its curved side.
- The area of each circular base is π * r^2, where r is the radius.
- The area of the curved side is the height times the circumference of the base, which is 2 * π * r.
The base of Box 3 has a radius of 2.5 inches, so the area of each base is π * (2.5)^2 = 19.63 square inches.
The curved side of Box 3 has a height of 12 inches, so the area of the curved side is 12 inches * (2 * π * 2.5) = 75.4 square inches.
Therefore, the total surface area of Box 3 is the sum of all face areas: 19.63 + 19.63 + 75.4 = 114.66 square inches.
The volume of a cylinder is found by multiplying the area of the base by the height.
- The volume of Box 3 is 19.63 square inches (base area) * 12 inches (height) = 235.56 cubic inches.
To determine the cost of making the box, assuming the cardboard costs 5 cents per square inch, multiply the surface area by the cost per square inch.
- The cost of making Box 3 would be 114.66 square inches * $0.05/square inch = $5.73.
In summary:
- Box 1 has a surface area of 258 square inches and a volume of 180 cubic inches. The cost of making Box 1 is $12.90.
- Box 2 has a surface area of 171.6 square inches and a volume of 192 cubic inches. The cost of making Box 2 is $8.58.
- Box 3 has a surface area of 114.66 square inches and a volume of 235.56 cubic inches. The cost of making Box 3 is $5.73.