Question

You want to make a rectangular prism out of cardboard. The base is 3 feet by 4 feet. The height is 2 feet. Cardboard costs $0.10 per square foot. How much money will it cost to make the prism?

Answer 1

The cost to make a rectangular prism out of cardboard with a base of 3 feet by 4 feet and a height of 2 feet is $5.20, based on the total surface area calculation using the cardboard price of $0.10 per square foot.

Step-by-step explanation:

To determine the cost of making a rectangular prism out of cardboard with the base dimensions of 3 feet by 4 feet, and a height of 2 feet, we need to calculate the surface area of the prism to find out how much cardboard is required. First, calculate the area of each face of the prism:

• Base and top (2 rectangles): 2 × (3 ft × 4 ft) = 24 sq ft
• Front and back (2 rectangles): 2 × (3 ft × 2 ft) = 12 sq ft
• Sides (2 rectangles): 2 × (4 ft × 2 ft) = 16 sq ft

Add the areas of all six faces to find the total surface area:

Total surface area = 24 sq ft + 12 sq ft + 16 sq ft = 52 sq ft

Since the cardboard costs $0.10 per square foot, we multiply the total surface area by the cost per square foot:

Cost = 52 sq ft × $0.10/sq ft = $5.20

Therefore, it will cost $5.20 to make the prism with the given dimensions using cardboard.

Answer 2

It would require $5.2 for the whole prism.

Step-by-step explanation:

The total cost required to make the prism will be the cost of the cardboard it requires to be purchased to make the cardboard.

Since it is given that

Length of cardboard = 3 feet

Width of cardboard = 4 feet

Height of cardboard = 2 feet

The total area required will be the sum of areas of the individual faces

1) Area of bottom face =
`length* width\\\\=3* 4=12feet^(2)`

2)Area of 4 side faces =
`2bh+2lh\\\\=2h(l+b)\\\\=2* 2* (4+3)\\\\=28ft^(2)`

3) Area of top face =
`length* width\\\\=3* 4=12feet^(2)`

Thus the total area required is =
`12+28+12=52ft^(2)`

Since it requires $0.10 per square foot hence it will require
`0.10* 52ft^(2)=5.2dollars`