A large washer has an outer radius of 10mm and a hole with a diameter of 14mm. What is the area of the top surface of the washer

The area of the washer's top surface, given its outer radius of 10 mm and a central hole diameter of 14 mm, is 160.29 mm².

Further Explanation

Area

• Area quantifies the extent of a two-dimensional surface.
• Calculating the area depends on the particular shape involved.

For instance:

• The area of a rectangle is found by multiplying length by width.
• The area of a triangle is computed as one half the base multiplied by the height.
• For a circle, area equals π times the radius squared, i.e., πr².
• The area of a square is the side length squared, s².

In this problem, the given large washer has an outer radius of 10 mm and an inner radius of 7 mm.

The annulus's area, representing the washer's surface, is calculated by:

Area = πR² − πr²

         = π(R² − r²)

where R is the outer radius and r is the inner radius.

Using π = 22/7, R = 10 mm, and r = 7 mm, we have:

Area = 22/7 × (10² − 7²)

         = 22/7 × (100 − 49) = 22/7 × 51

         = 160.29 mm²

Therefore, the washer's top surface area measures 160.29 mm².

Keywords: Area

Learn more about:

• Perimeter: brainly.com/question/1322653
• Area: brainly.com/question/1322653

Level: Middle school

Subject: Mathematics

Topic: Area and Perimeter

Answer:

The top surface area of the washer equals 160.14 square millimeters.

Step-by-step Explanation:

The washer's top surface forms an annulus, characterized by an outer radius of 10 mm and an inner radius of 7 mm (obtained since the hole's diameter is 14 mm and the radius is half the diameter).

Recall the formula for the area of an annulus:

where R is the outer radius and r the inner radius.

Substituting the given values:

Thus, the calculation yields: