Question

you need to replace the cover for a light in your bathroom. the light cover is a circle. the diameter of the light cover is 16 inches. what is the radius of the light cover? what is the circumference of the light cover? what is the area of the light cover? use the given information to complete the worksheet. use 3.14 as an approximation for π. diagram of a circle with points c, v, r diagram label | value | units radius of the light cover | | inches diameter of the light cover | | inches circumference of the light cover | | inches area of the light cover | | square inches 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:

Radius of the Light Cover

Step1: Recall radius-diameter relation

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

Step2: Substitute diameter value

Given \( d = 16 \) inches, then \( r=\frac{16}{2}=8 \) inches.

Diameter of the Light Cover

Step1: Identify given diameter

The problem states the diameter of the light cover is 16 inches.

Step2: Record the value

So the diameter is 16 inches.

Circumference of the Light Cover

Step1: Recall circumference formula

The circumference \( C \) of a circle is \( C = \pi d \) (or \( C = 2\pi r \)). Using \( \pi\approx3.14 \) and \( d = 16 \) inches.

Step2: Substitute values

\( C=3.14\times16 = 50.24 \) inches.

Area of the Light Cover

Answer:

s (for each part):

• Radius: \(\boldsymbol{8}\) inches
• Diameter: \(\boldsymbol{16}\) inches
• Circumference: \(\boldsymbol{50.24}\) inches
• Area: \(\boldsymbol{200.96}\) square inches