Question

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.

Answer 1

Glass 1 is a right circular cylinder and Glass 2 is a cone. The total volume of water in both the glasses is 100 centimeters cubed. Some given dimensions are:

Right Circular Cylinder:

diameter = 5, thus radius is half of that, radius =
`(5)/(2) = 2.5`cm

height = we need to find

(Note: Formula for volume, V, is
`\pi r^(2) h`)

Cone:

diameter = 6, thus radius is half of that, radius =
`(6)/(2) = 3` cm

height = 5.2 cm

(Note: Formula for volume, V, is
`(1)/(3) \pi r^(2) h`)

Now adding the 2 volumes and equating to 100, and then solving for h will give us our answer (we will use π as 3.14). Let's do this.

`\pi r^(2) h+(1)/(3) \pi r^(2) h=100\\(3.14)(2.5)^(2) h+(1)/(3) (3.14)(3)^(2) (5.2)=100\\19.625h+48.984=100\\19.625h=51.016\\h=(51.016)/(19.625)=2.60` cm. Hence height of glass 1 is 2.60 cm.

ANSWER: 2.60 cm