Volume Answers
The clubhouse has a water tank from which hikers fill their water jugs before walking the trail. The tank is a 5-gallon cylindrical container with a height of 2 feet and a radius of 4 inches. Alex fills his 1-gallon jug from the clubhouse tank before going on a hike. If the 5-gallon tank was full, what was the height of the water in the tank after Alex filled the 1-gallon jug?
A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for and “r^2” for .
Reponses may vary but should include some or all of the following information: The original volume of the cone is V= (1/3)pi(r^2)h. Tripling the radius (3r) and halving the height (h/2), we get a new volume of V=(1/3)pi(3r)^2(h/2), or V=(3/2)pi(r^2)h. Thus, the cone’s volume has increased by a factor of (3/2)/(1/3) = 9/2, or 4.5. The original volume of the cylinder is V=pi(r^2)h. Doubling the height, we get a new volume of V=pi(r^2)(2h) = 2pi(r^2)h. Thus, the cylinder’s volume has increased by a factor of 2/1, or 2. Therefore, the changes produced a greater increase in volume in the cone than in the cylinder.
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