Chapter 11, Problem 3E

To determine

To compute area of the metal washer.

Answer to Problem 3E

  $293.8$ squaremillimeters.

Explanation of Solution

Given information:

Diameter of larger disc $D=9+5.5+5.5$

  $=20$ millimeters. Hence radius $R=\frac{D}{2}$

  $=\frac{20}{2}=10$ millimeters.

Diameter of the cut out smaller disc $d=9$ millimeters. Hence radius $r=\frac{d}{2}$

  $=\frac{9}{2}=4.5$ millimeters.

Formula used:

Area of circle $A=\pi \times r^2$

For calculations, value of $\pi =3.14$

Calculation:

To calculate the area of the metal washer, subtract the area of the smaller cut out circular portion from the area of the large circular metallic disc.

  $A-a=\pi \times R^2-\pi \times r^2$

Subtraction of the two respective areas.

  $=\pi \left(R^2-r^2\right)$

On simplifying the equation.

  $=3.14\times \left({10}^2-{4.5}^2\right)$

Putting values of radii in the expression.

  $=3.14\times \left(100-20.25\right)$

Expanding the square of the radii.

  $=3.14\times 79.75$

Multiply the result with the value of pi.

  $=293.75$

Rounding to the nearest tenth.

  $=293.8$ square millimeters.