Question

a local restaurant places lids on children’s cups.
the diameter of the cup lid is 84 millimeters.
what is the radius of the cup lid? what is the circumference of the cup lid? what is the area of the cup lid?
use the given information to complete the worksheet. use 3.14 as an approximation for \\(\pi\\).
diagram label | value | units
radius of the cup lid | id | millimeters
diameter of the cup lid | ld | 84 | millimeters
circumference of the cup lid | | millimeters
area of the cup lid | | square millimeters
area formulas:

• parallelogram: \\(a = bh\\)
• square: \\(a = s^2\\)
• triangle: \\(a = \frac{1}{2} bh\\)
• trapezoid: \\(a = \frac{1}{2} h(b_1 + b_2)\\)
• circle: \\(a = \pi r^2\\)

Explanation:

Step1: Find the radius

The radius \( r \) of a circle is half of its diameter \( d \). Given \( d = 84 \) millimeters, so \( r=\frac{d}{2}=\frac{84}{2} = 42 \) millimeters.

Step2: Find the circumference

The formula for the circumference \( C \) of a circle is \( C=\pi d \) (or \( C = 2\pi r \)). Using \( \pi\approx3.14 \) and \( d = 84 \), we have \( C=3.14\times84=263.76 \) millimeters.

Step3: Find the area

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). We know \( r = 42 \) and \( \pi\approx3.14 \), so \( A = 3.14\times42^{2}=3.14\times1764 = 5538.96 \) square millimeters.

Answer:

• Radius of the Cup Lid: \( 42 \) millimeters
• Circumference of the Cup Lid: \( 263.76 \) millimeters
• Area of the Cup Lid: \( 5538.96 \) square millimeters