An artist wants to use silver wire to make a square that has a side length of 16 inches, then use copper wire to make the largest circle that can possibly fit in the square. At the local jewelry store, the artist can purchase silver wire for $8.75/ft and copper wire for $6.50/10ft (the wire is only sold in the increments noted in the price). The artist would like a detailed cost analysis of the project.

Question

An artist wants to use silver wire to make a square that has a side length of 16 inches, then use copper wire to make the largest circle that can possibly fit in the square. At the local jewelry store, the artist can purchase silver wire for $8.75/ft and copper wire for $6.50/10ft (the wire is only sold in the increments noted in the price). The artist would like a detailed cost analysis of the project.

Can someone start me up? What do i have to do?

Answer 1

make your sketch,

the side of the square is 16 inches or 4/3 ft
O you will need 16/3 ft for the square
cost of that in silver is (16/3)(8.75) dollars

the circle will have a diameter of 4/3 ft
and its cost = (4/3)π(6.5/10) dollars

continue

Answer 2

Thank you, i got the answer

Answer 3

To calculate the cost analysis of the project, you need to determine the amount of each type of wire required, calculate the total length needed, and then multiply it by the respective cost per foot/increment.

Let's start with the square made of silver wire:

1. Determine the perimeter of the square:
Since all sides of a square are equal, the perimeter is given by: 4 * side length.
In this case, the side length of the square is 16 inches. So, the perimeter would be 4 * 16 = 64 inches.

2. Determine the length of silver wire needed:
Since the perimeter is equal to the length of wire required for the square, the length needed would be 64 inches.

3. Convert the length to feet:
Divide the length in inches by 12 to convert it to feet.
In this case, 64 inches / 12 = 5.33 feet.

4. Calculate the cost of silver wire:
The cost per foot of silver wire is $8.75.
Multiply the cost per foot by the length needed (in feet) to get the total cost of silver wire:
$8.75/ft * 5.33 ft = $46.57 (rounded to the nearest cent).

Now, let's move on to the circle made of copper wire:

1. Determine the diameter of the circle:
The diameter of the circle is equal to the side length of the square.
In this case, the diameter would also be 16 inches.

2. Determine the radius of the circle:
The radius is half the diameter.
In this case, the radius would be 16 inches / 2 = 8 inches.

3. Determine the length of copper wire needed:
The circumference of a circle can be calculated using the formula: 2 * π * radius.
In this case, the length of copper wire needed would be 2 * 3.14 * 8 inches.

4. Convert the length to feet:
Divide the length in inches by 12 to convert it to feet.
In this case, (2 * 3.14 * 8) inches / 12 = 4.19 feet.

5. Calculate the cost of copper wire:
The copper wire is sold in increments and costs $6.50 for every 10 feet.
To determine the cost, divide the length needed by the increment (10 feet) and round up to the nearest whole number.
In this case, 4.19 feet / 10 feet = 0.42 (round up to 1).

Multiply the number of increments (1) by the cost per increment ($6.50) to get the total cost of copper wire:
1 increment * $6.50 = $6.50.

Therefore, the detailed cost analysis of the project is as follows:
- Silver wire cost: $46.57
- Copper wire cost: $6.50

The total cost of the project would be $46.57 + $6.50 = $53.07.