considering the area of a circular ring as a increment of area of a circle, find approximately the area of a ring whose inner and outer radii are 3 inches and 3.02 inches, respectively.
Formula to find area of circle=(3.14*r2)/2 as r is inches . Their units will also be in inches.
Area = dc/dt =2(pi)r(dr/dt)
= 2(pi)(3)(0.02)
= 0.377 in2
To find the area of a circular ring, we need to subtract the area of the inner circle from the area of the outer circle.
Step 1: Find the area of the inner circle:
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
Using the given inner radius of 3 inches, we can calculate the area of the inner circle as:
A_inner = π * (3 inches)^2
Step 2: Find the area of the outer circle:
Using the given outer radius of 3.02 inches, we can calculate the area of the outer circle as:
A_outer = π * (3.02 inches)^2
Step 3: Calculate the area of the ring:
To find the area of the ring, we need to subtract the area of the inner circle from the area of the outer circle:
A_ring = A_outer - A_inner
Step 4: Calculate the approximate area of the ring:
To get an approximate value, we can use the value of π as 3.14. So we have:
A_ring = 3.14 * (3.02 inches)^2 - 3.14 * (3 inches)^2
Using a calculator, we can now solve this equation to find the approximate area of the ring.
To find the approximate area of a circular ring, we need to find the difference in areas between the outer and inner circles. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
First, let's find the area of the outer circle with a radius of 3.02 inches:
A_outer = π(3.02)^2
Now, let's find the area of the inner circle with a radius of 3 inches:
A_inner = π(3)^2
To find the area of the ring, we subtract the area of the inner circle from the area of the outer circle:
A_ring = A_outer - A_inner
Let's calculate the approximate area of the ring:
A_outer = π(3.02)^2
= 3.14159 * (3.02)^2
≈ 28.647 sq inches (rounded to 3 decimal places)
A_inner = π(3)^2
= 3.14159 * (3)^2
≈ 28.274 sq inches (rounded to 3 decimal places)
A_ring ≈ A_outer - A_inner
≈ 28.647 - 28.274
≈ 0.373 sq inches (rounded to 3 decimal places)
Therefore, the approximate area of the ring with inner and outer radii of 3 inches and 3.02 inches, respectively, is approximately 0.373 square inches.