Question

The circumference of the hub cap of a tire is 83.21 centimeters. Find the area of this hub cap. Use

3.14 for . Use pencil and paper. If the circumference of the hub cap were smaller, explain how this
would change the area of the hub cap.
The area of this hub cap is about square centimeters.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest
thousandth as needed.)

Answer 1

551 square centimeters

Explanation:

Finding the radius (r) :

• C = 2πr
• 83.21 = 2 x 3.14 x r
• 83.21 = 6.28r
• r = 83.21/6.28
• r = 13.25 cm

Finding the area :

• A = πr²
• A = 3.14 x (13.25)²
• A = 3.14 x 175.5625
• A = 551 square centimeters (nearest whole number)

The area of this hub cap is about 551 square centimeters.

Answer 2

Area = 551 cm² (nearest whole number)

Explanation:

Circumference

`\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}`

Given:

• Circumference = 83.21 cm
• π = 3.14

Substituting the given values into the formula and solving for r:

`\begin{aligned}\implies \sf 83.21 & =\sf 2 \cdot 3.14 \cdot r\\\\\sf r & = \sf (83.21)/(2 \cdot 3.14)\\\\\sf r & = \sf 13.25\:cm\end{aligned}`

Area

`\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}`

Given:

• r = 13.25 cm
• π = 3.14

`\begin{aligned}\implies \sf Area & =\sf 3.14 \cdot 13.25^2\\\\& = \sf 551\:cm^2\:(nearest\:whole\:number)\end{aligned}`

If the circumference of the hub cap was smaller, the radius would be smaller, hence the area would be smaller.