How to Find Surface Area of a Circle with Removed Sector | Step-by-Step Guide

[mitz_fitz]

if some people could please allow me to bounce answers off them and show them my work by means of e-mail before I send it away to be marked, it would be highly appreciated, thanks

one problem I have at the moment is I need to find the surface area of a circle after a sector has been removed
the circle has a radius of 750mm and the segment is 36 degrees wide at the edge of the circle

thanks,
reuben

contact me directly mitz_fitz@hotmail.com

 

[whozum]

Removing a sector of a circle with an arc of 36 degrees gives 9/10 the area of the full circle. 36 degrees is (360-36)/360 = 324/360 = 9/10. Thus the net area is

$$\pi r^2 - \frac{\pi}{10} r^2$$ with r = 750mm.

 

[tacman]

Hi Reuben,

Thank you for reaching out for help with finding the surface area of a circle with a removed sector. I would be happy to assist you and review your work before you submit it for marking. Let's go through the steps together to make sure you understand the process.

Step 1: Understand the Formula

The formula for finding the surface area of a circle is A = πr^2, where A is the surface area and r is the radius of the circle. However, since we have a removed sector, we need to modify the formula to account for the missing portion of the circle.

Step 2: Find the Area of the Full Circle

First, we need to find the area of the full circle using the given radius of 750mm. Plugging this value into the formula, we get A = π(750)^2 = 1,767,145.87 mm^2.

Step 3: Find the Area of the Removed Sector

Next, we need to find the area of the removed sector. To do this, we need to find the central angle of the sector using the given angle of 36 degrees. Since we know that the circumference of a circle is 360 degrees, we can set up a proportion to find the central angle as follows:

36/360 = x/2πr

Solving for x, we get x = (36/360)(2π)(750) = 47.12 mm.

Now, we can use the formula for the area of a sector, A = (θ/360)πr^2, where θ is the central angle and r is the radius. Plugging in the values, we get A = (47.12/360)π(750)^2 = 7,725.47 mm^2.

Step 4: Subtract the Area of the Removed Sector

Finally, we can subtract the area of the removed sector from the area of the full circle to get the surface area of the circle with the removed sector. So, the final formula would be A = πr^2 - (θ/360)πr^2. Plugging in the values, we get A = 1,767,145.87 - 7,725.47 = 1,759,420.40 mm^2.

Step 5: Double Check Your Work

It is always a good idea to double check your work to ensure accuracy