Cylindrical Rod Radius Calculation

The problem requires us to calculate the radius of a cylindrical rod using its given curved surface area and length. We need to apply the standard formula for the curved surface area of a cylinder and solve for the radius.

Given Information Analysis

Let's list the information provided:

• Curved Surface Area ($A$) = $4,900 \text{ cm}^2$
• Length of the rod (Height, $h$) = $97 \text{ cm}$
• The value of $\pi$ to be used is $\frac{22}{7}$

Formula for Curved Surface Area

The formula for the curved surface area ($A$) of a cylinder is:

$$A = 2 \pi r h$$

Where:

• $A$ represents the curved surface area
• $\pi$ is the mathematical constant Pi
• $r$ is the radius of the cylinder's base
• $h$ is the height (or length) of the cylinder

Step-by-step Calculation

To find the radius ($r$), we need to rearrange the formula:

$$r = \frac{A}{2 \pi h}$$

Now, substitute the given values into the formula:

$$r = \frac{4900}{2 \times \frac{22}{7} \times 97}$$

First, calculate the value of $2 \pi h$:

$$2 \times \frac{22}{7} \times 97 = \frac{44}{7} \times 97$$

Multiply 44 by 97:

$$44 \times 97 = 4268$$

So, $2 \pi h = \frac{4268}{7}$.

Now, substitute this back into the equation for $r$:

$$r = \frac{4900}{\frac{4268}{7}}$$

To divide by a fraction, we multiply by its reciprocal:

$$r = 4900 \times \frac{7}{4268}$$

$$r = \frac{4900 \times 7}{4268}$$

$$r = \frac{34300}{4268}$$

Now, perform the division:

$$r \approx 8.03655...$$

Rounding to Two Decimal Places

The question asks for the radius correct to two decimal places. We look at the third decimal place, which is 6. Since 6 is 5 or greater, we round up the second decimal place.

$$r \approx 8.04 \text{ cm}$$

Therefore, the radius of the rod is approximately $8.04$ cm.