A golden wedding ring is 20mm in diameter and has a 14mm hole in the middle
A. What is the area of the ring
B. What is the cost of the ring if 1mmsquare of gold is equivalent to 5gh
Area = pi r^2 r = d/2
A. pi (10^2 - 7^2) = ?
B. Need volume rather than area. What is the thickness of the ring?
B. Assuming standardized ring pricing, as indicated by the price of 5gh/mm^2, then the cost is 5*(A) from above
To solve this problem, we need to find the area of the ring and then find the cost based on the area.
A. To find the area of the ring, we need to subtract the area of the hole from the area of the outer ring.
The area of the outer ring can be calculated using the formula for the area of a circle, which is A = πr^2, where r is the radius of the circle. The diameter of the outer ring is 20mm, so the radius is half of that, which is 10mm.
Therefore, the area of the outer ring is A = π(10mm)^2.
The area of the hole can also be calculated using the same formula, but with the diameter of the hole. The hole has a diameter of 14mm, so the radius is 7mm.
Therefore, the area of the hole is A = π(7mm)^2.
Now we can find the area of the ring by subtracting the area of the hole from the area of the outer ring:
Area of the ring = Area of outer ring - Area of hole
= π(10mm)^2 - π(7mm)^2
B. To find the cost of the ring, we need to know the total area of the ring and the cost of 1mm^2 of gold.
Let's assume that the area of the ring is in mm^2.
If 1mm^2 of gold is equivalent to 5gh, then the cost of the ring can be calculated as:
Cost of the ring = Total area of the ring * Cost of 1mm^2 of gold
Please provide the value of the radius of the hole, so we can continue with the calculation and provide you with the final answer.
To answer the questions, we need to find the area of the ring and then calculate the cost based on the price per square millimeter of gold.
A. To find the area of the ring, we first need to calculate the area of the larger circle (outer edge) and then subtract the area of the smaller circle (inner hole).
1. Calculate the area of the larger circle (outer edge):
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
The diameter of the ring is 20mm, so the radius (r) is half of that, which is 10mm.
Substitute the values into the formula: A = π(10mm)^2 = 100π mm^2
2. Calculate the area of the smaller circle (inner hole):
The diameter of the hole is 14mm, so the radius (r) is half of that, which is 7mm.
Substitute the values into the formula: A = π(7mm)^2 = 49π mm^2
3. Subtract the area of the smaller circle from the area of the larger circle to get the area of the ring:
Area of the ring = Area of larger circle - Area of smaller circle = 100π mm^2 - 49π mm^2 = 51π mm^2
So, the area of the ring is 51π mm^2.
B. To calculate the cost of the ring, we need to know the price per square millimeter of gold.
Let's assume the price per square millimeter of gold is given as 5gh (gh represents a fictional currency unit).
To find the cost of the ring, we need to multiply the area of the ring by the price per square millimeter.
Cost of the ring = Area of the ring * Price per square millimeter
Cost of the ring = 51π mm^2 * 5gh
If you have the value of π (pi) and the price per square millimeter of gold, you can multiply them to get the cost of the ring in gh.