Question

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

Answer 1

Answer:

Area = 551 cm² (nearest whole number)

Step-by-step 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:

$\begin{aligned}\implies \sf 83.21 & =\sf 2 \cdot 3.14 \cdot r\\\\\sf r & = \sf \dfrac{83.21}{2 \cdot 3.14}\\\\\sf r & = \sf 13.25\:cm\end{aligned}$

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.

Answer 2

Answer:

551 square centimeters

Step-by-step 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.