Questions: Find the total surface area of the right circular cylinder with r=755 m and h=259 m. A= [square] m^2 (Round to the nearest ten thousand as needed.)

Transcript text: Find the total surface area of the right circular cylinder with $\mathrm{r}=755 \mathrm{~m}$ and $\mathrm{h}=259 \mathrm{~m}$. $A=$ $\square$ $\mathrm{m}^{2}$ (Round to the nearest ten thousand as needed.)

Solution

Solution Steps

Step 1: Formula for the Total Surface Area of a Cylinder

The total surface area (A) of a right circular cylinder is given by the formula: A = 2πr² + 2πrh, where r is the radius and h is the height.

Step 2: Substitute the Given Values

We are given r = 755 m and h = 259 m. Substituting these values into the formula, we have:

A = 2π(755)² + 2π(755)(259)

Step 3: Calculate the Surface Area

A = 2π(570025) + 2π(195545) A = 1140050π + 391090π A = 1531140π A ≈ 4811780.243

Step 4: Round to the Nearest Ten Thousand

Rounding to the nearest ten thousand, we get 4,810,000.

Final Answer:

The total surface area is approximately 4,810,000 m².

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