Phapter 8: Volumes of cyllnders > Section Exercises \( 8.1> \) Exerclse 18 A tank on a road roller is filled with water to make the roller heavy. The tank is a cylinder that has a height of 6 feet and a radius of 2 feet. One cubic foot of water weighs 62.5 pounds. Find the weight of the water in the tank. To the nearest whole number, the water weighs pounds.

To find the weight of the water in the cylindrical tank, we first need to determine the volume of the cylinder. The formula for the volume \(V\) of a cylinder is given by: \[ V = \pi r^2 h \] Where \(r\) is the radius (2 feet), and \(h\) is the height (6 feet). Plugging in the values: \[ V = \pi (2^2)(6) = \pi (4)(6) = 24\pi \] Now, we approximate \( \pi \) as 3.14: \[ V \approx 24 \times 3.14 \approx 75.36 \text{ cubic feet} \] Next, to find the weight, we multiply the volume by the weight of one cubic foot of water (62.5 pounds): \[ \text{Weight} = 75.36 \times 62.5 \approx 4708.75 \text{ pounds} \] Rounding to the nearest whole number, the water weighs approximately **4709 pounds**. If you ever need to find the volume of a cylinder, remember the secret combo: multiply the area of the base (which is a circle) by the height! It’s like making a tall drink – just build that base and pour! Mistakes often happen when forgetting to convert units or misuse the height and radius, but with practice, you'll be a volume pro in no time! The beauty of shapes like cylinders doesn't just live in math! They’re everywhere in real life! Think about water towers and soda cans – they’re all cylindrical! Understanding how to calculate their volumes can help in practical applications, like figuring out how much liquid a container can hold, which is super handy in cooking or construction projects.