Question

Ellen filled the glasses shown below completely with water. The total amount of water that Ellen poured into the glasses is 200 cubic centimeters. What is the height of glass 1? Round your answer to the nearest hundredths. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale.

A cylinder with width 6.2 and height unknown is labeled glass 1, and a cone with height 7.3 and width 6.4 is labeled glass 2.

0.20 centimeters
4.04 centimeters
3.92 centimeters
5.64 centimeters

Answer 1

h=4.04 cm.

Explanation:

Answer 2

Answer=4.04

Volume in both glasses = Volume (glass 1) + Volume (glass 2)

Volume (glass 1) = πr²h

r= 6.2/2 = 3.1 cm

Volume (glass 1) = πr²h = (3.1)²πh= 9.61πh

Volume (glass 2) = (1/3)πR²H

R= 6.4/2 = 3.2 cm

H = 7.3 cm

Volume (glass 2) = (1/3)πR²H= (1/3)π(3.2)² * 7.3 = (74.752/3)π

Volume in both glasses = πr²h + (1/3)πR³H

200 = 9.61πh + (74.752/3)π

9.61πh= 200 - (74.752/3)π

h= (200 - (74.752/3)π)/(9.61π) ≈ 4.03 cm

Answer is h=4.04 cm.