Question

Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60 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.

The possible answers are 0.2, 1.7, 3.9 or 5.6. When googled the answer always comes up 3.9. I always get 1.6527 which rounds up to 1.7. How about you?

Answer 1

The height of glass 1 is 1.7 cm.

Explanation:

We are given the following information in the question:

The total amount of water that Samuel poured into the glasses is 60 cubic centimeters.

Volume of glass 2 = Volume of cone =

`\displaystyle(1)/(3)\pi r^2h\\\\\text{Putting value of r and h}\\\\= (1)/(3)* 3.14* (5)/(2)* (5)/(2)* 6 = 39.25\text{ cubic cm}`

Volume of glass 1 =

`\text{ Total Volume } - \text{Volume of glass 2}\\= 60 - 39.25\\= 20.75\text{ cubic cm}`

Volume of glass 1 = Volume of cylinder =

`20.75 = \pi r^2h\\\text{where r is the radius of cylinder and h is the height of cylinder}\\\\\text{Putting the values of r}\\\\  20.75 = 3.14* \displaystyle(4)/(2)* (4)/(2)* h\\\\h = (20.75)/(3.14* 2* 2) 1.656 \approx 1.7`

Thus, the height of glass 1 is 1.7 cm.

Answer 2

volume of glass 2 = pi*r^2*h/3= 3.14 *2.5^2*6/3 = 39.25 cubic cm

60-39.25 = 20.75 cu cm was in 1st cup

volume of cylinder = pi *r^2 *h

20.75 = 3.14 *2^2 *h

20.75 = 3.14*4*h

20.75 = 12.56*h

h = 20.75 /12.56 = 1.652 round to 1.7