Respuesta :
Answer:
The area of the top surface of the washer is: 160.14 square mm.
Step-by-step explanation:
The top of the surface is in the shape of a annulus with a outer radius of 10 mm and a inner radius of 7 mm ( since the diameter of the hole is: 14 mm and we know that the radius is half of the diameter)
Now, we know that the area of the annulus region is given by:
[tex]Area=\pi (R^2-r^2)[/tex]
where R is the outer radius and r is the inner radius.
Here we have:
[tex]R=10\ mm\\\\and\\\\r=7\ mm[/tex]
Hence, we have:
[tex]Area\ of\ top\ surface=\pi (10^2-7^2)\\\\i.e.\\\\Area\ of\ top\ surface=\pi (100-49)\\\\i.e.\\\\Area\ of\ top\ surface=\pi\cdot 51\\\\i.e.\\\\Area\ of\ top\ surface=160.14\ mm^2[/tex]
The area of the top surface of a washer with an outer radius of 10 mm and a hole with a diameter of 14 mm is 160.29 mm².
Further Explanation
Area
- Area is a measure of how much space is occupied by a given shape.
- Area of a substance is determined by the type of shape in question.
For example;
- Area of a rectangle is given by; Length multiplied by width
- Area of a triangle = 1/2 x base x height
- Area of a circle = πr² where r is the radius of a circle,
- Area of a square = S², Where s is the side of the square, etc.
In this question, we are given a large washer with an outer radius of 10 mm and inner radius of 7 mm.
Area of annulus region will be given by;
Area = πR²- πr²
= π(R²-r²)
Where R is the outer radius while r is the inner radius.
Therefore; Taking π = 22/7, R = 10 mm and r = 7 mm
Area = 22/7( 10²-7²)
= 22/7 (51)
= 160.29 mm²
Therefore, the area of the top surface of the large washer is 160.29 mm².
Keywords: Area
Learn more about;
- Perimeter: https://brainly.com/question/1322653
- Area : https://brainly.com/question/1322653
Level: Middle school
Subject; Mathematics
Topic: Area and Perimeter
