1 Multiple choice 14 points A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. Which measurement is closest to the total surface area of the can in square centimeters? (O) \( 245.04 .19 \mathrm{~cm}^{2} \)

The total surface area \(A\) of a cylinder can be calculated using the formula \(A = 2\pi r(h + r)\), where \(r\) is the radius and \(h\) is the height. With a diameter of 6 cm, the radius \(r\) is 3 cm, and the height \(h\) is 10 cm. Plugging in the numbers: \[ A = 2\pi(3)(10 + 3) = 2\pi(3)(13) \approx 245.04 \text{ cm}^2. \] So, the closest measurement to the total surface area of the can is indeed \(245.04 \text{ cm}^2\). Calculating the surface area of a cylinder helps us understand not only the physical dimensions of everyday objects but also practical applications like when designing cans for beverages or food. Engineers use these calculations to optimize material use while ensuring the can remains durable and functional! If you're calculating surface areas in real life, one common mistake is forgetting to convert units. For instance, if one measurement is in centimeters and another in meters, you'll need to convert them to the same unit before performing your calculations to avoid inaccuracies. Always double-check that all dimensions are in the same unit!