Mona filled the glasses shown below completely with water. The total amount of water that Mona poured into the glasses is 100 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale. (1 point)
A cylinder with width 5 and height unknown is labeled glass 1, and a cone with height 5.2 and width 6 is labeled glass 2.
2.6 centimeters
4.8 centimeters
5.6 centimeters
7.4 centimeters
To find the height of glass 1, we need to equate the volume of the cylinder to 100 cubic centimeters.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height. Since the width of glass 1 is given as 5, we can assume that the radius is half of the width: r = 5/2 = 2.5.
Therefore, the volume of glass 1 is V1 = π(2.5)^2h.
On the other hand, the volume of glass 2 is given as 100 cubic centimeters, so V2 = (1/3)π(3^2)(5.2) = (20/3)π.
Equating the volumes, we have:
V1 = V2
π(2.5)^2h = (20/3)π
(2.5)^2h = (20/3)
6.25h = 20/3
h = (20/3)(1/6.25)
h = 20/18.75
h ≈ 1.07
Rounding to the nearest tenth, the height of glass 1 is approximately 1.1 centimeters.
Therefore, the answer is 2.6 centimeters.