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Chapter 1: Problem 41

What is the surface area of a right cylinder of height \(20.5 \mathrm{~cm}\) and radius \(11.9 \mathrm{~cm} ?\)

Short Answer

Expert verified
Answer: The approximate surface area of the right cylinder is 2422.79 cm².

Step by step solution

01

Identify the given values

The given values in the exercise are: - Height of the cylinder, \(h = 20.5 \mathrm{~cm}\) - Radius of the base, \(r_\text{base} = 11.9 \mathrm{~cm}\)
02

Apply the surface area formula

Now use the surface area formula as follows: \(A_\text{cylinder} = 2\pi r_\text{base}^2 + 2\pi r_\text{base} h\)
03

Substitute the given values into the formula

Plug the given height and radius values into the formula: \(A_\text{cylinder} = 2\pi (11.9)^2 + 2\pi (11.9)(20.5)\)
04

Calculate

Perform the calculations to find the surface area: \(A_\text{cylinder} = 2\pi (141.61) + 2\pi (243.95)\) \(A_\text{cylinder} = 283.22\pi + 487.9\pi \) \(A_\text{cylinder} = 771.12\pi\)
05

Convert to the approximate value

Multiply by the value of pi (approximately \(3.14\)) to get the final result: \(A_\text{cylinder} \approx 771.12 \times 3.14 \approx 2422.79 \mathrm{~cm}^2\) So the surface area of the right cylinder is approximately \(2422.79 \mathrm{~cm}^2\).

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