A golden ring is 20mm in diameter and has a 14mm hole in the middle.i). What is the area of the ring[Take π=22/7].ii.) If 1mmsquare of gold costs gh5.00,Calculate the cost of the ring.

area= π/4 (10^2 - 7^2) = 51π/4

cost = 5 * area/1 = 255π/4

d = outer diameter

D = inside diameter

Area = Area of ​​outer diameter - area of ​​inner diameter

A = d² π / 4 - D² π / 4

A = ( d² - D² ) π / 4

A = ( 20² - 14² ) π / 4

A = ( 400 - 196 ) π / 4

A = 204 • π / 4

A = 50 π

A = 50 • 22 / 7 = 1100 / 7

A = 157.1428571428571 mm²

Gold is paid by volume, not by area.

To find the area of the ring, we need to subtract the area of the hole from the area of the outer ring.

i) The area of the ring can be calculated as follows:

Area of the ring = Area of outer circle - Area of inner circle

The formula for the area of a circle is A = πr^2, where π is approximately 22/7.

Given:
Diameter of the ring = 20mm
Radius of the outer circle = diameter/2 = 20/2 = 10mm

So, the area of the outer circle = π * (radius)^2 = (22/7) * (10)^2 = 314.29 mm^2 (rounded to two decimal places).

Radius of the inner circle (hole) = 14/2 = 7mm

So, the area of the inner circle = π * (radius)^2 = (22/7) * (7)^2 = 154 mm^2 (rounded to two decimal places).

Finally, the area of the ring = Area of outer circle - Area of inner circle
= 314.29 - 154
= 160.29 mm^2 (rounded to two decimal places).

ii) To calculate the cost of the ring, we need to know the total amount of gold used, which is equal to the area of the ring.

Given:
1 mm^2 of gold costs GH₵5.00

So, to find the cost of the ring, we multiply the area of the ring by the cost of 1 mm^2 of gold.

Cost of the ring = Area of the ring * Cost of 1 mm^2 of gold

Using the calculated area of the ring (160.29 mm^2):

Cost of the ring = 160.29 * GH₵5.00 = GH₵801.45 (rounded to two decimal places).

Therefore, the cost of the ring is GH₵801.45.

To find the area of the ring and the cost of the ring, we can break down the problem into smaller steps.

i) Finding the area of the ring:
The ring consists of an outer circle and an inner circle. We can calculate the area of the ring by subtracting the area of the inner circle from the area of the outer circle.

1. Calculate the radius of the outer circle:
The diameter of the ring is given as 20mm. To find the radius, divide the diameter by 2:
Radius = 20mm / 2 = 10mm.

2. Calculate the area of the outer circle:
The formula for the area of a circle is A = πr², where A is the area and r is the radius.
Area of outer circle = π(10mm)² = 100π mm².

3. Calculate the radius of the inner circle:
The diameter of the hole in the middle is given as 14mm. To find the radius, divide the diameter by 2:
Radius = 14mm / 2 = 7mm.

4. Calculate the area of the inner circle:
Area of inner circle = π(7mm)² = 49π mm².

5. Calculate the area of the ring:
Area of ring = Area of outer circle - Area of inner circle = 100π mm² - 49π mm² = 51π mm².

Using the given value of π = 22/7, we can approximate the area of the ring:
Area of ring = 51π mm² ≈ 51 * (22/7) mm².

ii) Calculating the cost of the ring:
Now that we have the area of the ring, we can calculate the cost based on the cost per square millimeter.

1. Calculate the cost per square millimeter:
Given that 1mm² of gold costs GH₵5.00.

2. Calculate the cost of the ring:
Cost of the ring = Area of ring * Cost per square millimeter.

Substituting the known values:
Cost of the ring = 51 * (22/7) mm² * GH₵5.00.

You can now calculate the final cost by multiplying the area of the ring by the cost per square millimeter.