Questions: The length (in centimeters) of a bearing in the shape of a cylinder is given by (150.72/pi r^2), where r is the radius of the base of the cylinder. Find the length of a bearing with a diameter of 8 centimeters, using 3.14 as an approximation of pi. The length of the bearing is cm. (Simplify your answer.)

The length (in centimeters) of a bearing in the shape of a cylinder is given by (150.72/pi r^2), where r is the radius of the base of the cylinder. Find the length of a bearing with a diameter of 8 centimeters, using 3.14 as an approximation of pi.

The length of the bearing is cm. (Simplify your answer.)

Transcript text: Homework: P-5 pressions Question 16, P.5.99 HW Score: 88.24\%, 15 of 17 points Points: 0 of 1 Save The length (in centimeters) of a bearing in the shape of a cylinder is given by $\frac{150.72}{\pi r^{2}}$, where $r$ is the radius of the base of the cylinder. Find the length of a bearing with a diameter of 8 centimeters, using 3.14 as an approximation of $\pi$. The length of the bearing is $\square$ cm. (Simplify your answer.) Incorrect: 0

Solution

Solution Steps

Step 1: Calculate the Radius

Given the diameter $ d = 8 $ cm, the radius $ r $ can be calculated as: \[ r = \frac{d}{2} = \frac{8}{2} = 4 \text{ cm} \]

Step 2: Substitute into the Length Formula

The formula for the length $ L $ of the bearing is given by: \[ L = \frac{150.72}{\pi r^{2}} \] Substituting $ r = 4 $ cm and using $ \pi \approx 3.14 $: \[ L = \frac{150.72}{3.14 \cdot (4)^{2}} = \frac{150.72}{3.14 \cdot 16} \]

Step 3: Simplify the Expression

Now, we simplify the expression: \[ L = \frac{150.72}{50.24} = 3 \text{ cm} \]