A company is making two types of aluminum containers. One is a cylinder with a height of 1.25 feet and a diameter of 1 foot. The other is a rectangular prism with a length of 0.75 foot, a width of 0.75 foot, and a height of 1 foot. Aluminum costs $.02 per square foot. How much will it cost to produce each type of container? Round to the nearest cent. Which container holds more?
I posted this yesterday and you haven't responded to my questions. Do you want help --or are you just trying to mooch answers?
You've posted this before.
Have you found the surface area of the cylinder?
Have you found the surface area of the rectangular prism?
I'll be glad to check those answers.
To calculate the cost of producing each type of container, we need to find the surface area of each container and then multiply it by the cost of aluminum per square foot.
Let's start with the cylinder:
1. Calculate the surface area of the cylinder:
- The formula for the surface area of a cylinder is A = 2πr^2 + 2πrh, where r is the radius and h is the height.
- The diameter of the cylinder is given as 1 foot, so the radius (r) is half of that, which is 0.5 feet.
- Plugging in the values, A = 2π(0.5^2) + 2π(0.5)(1.25).
- Simplifying, A = π(0.25) + 2.5π = 0.25π + 2.5π = 2.75π square feet.
2. Calculate the cost of aluminum for the cylinder:
- The cost of aluminum per square foot is given as $0.02.
- Multiply the surface area of the cylinder by the cost per square foot: Cost = 2.75π * $0.02.
Now let's move on to the rectangular prism:
1. Calculate the surface area of the rectangular prism:
- The formula for the surface area of a rectangular prism is A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
- Plugging in the values, A = 2(0.75)(0.75) + 2(0.75)(1) + 2(0.75)(1) = 1.5 + 1.5 + 1.5 = 4.5 square feet.
2. Calculate the cost of aluminum for the rectangular prism:
- The cost of aluminum per square foot is given as $0.02.
- Multiply the surface area of the rectangular prism by the cost per square foot: Cost = 4.5 * $0.02.
Finally, compare the costs and determine which container holds more:
- Round the costs to the nearest cent.
- Compare the rounded costs to see which container is more expensive.
Hope this helps!