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 = [tex]\frac{5}{2} = 2.5[/tex]cm
height = we need to find
(Note: Formula for volume, V, is [tex]\pi r^{2} h[/tex])
Cone:
diameter = 6, thus radius is half of that, radius = [tex]\frac{6}{2} = 3[/tex] cm
height = 5.2 cm
(Note: Formula for volume, V, is [tex]\frac{1}{3} \pi r^{2} h[/tex])
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.
[tex]\pi r^{2} h+\frac{1}{3} \pi r^{2} h=100\\(3.14)(2.5)^{2} h+\frac{1}{3} (3.14)(3)^{2} (5.2)=100\\19.625h+48.984=100\\19.625h=51.016\\h=\frac{51.016}{19.625}=2.60[/tex] cm. Hence height of glass 1 is 2.60 cm.
ANSWER: 2.60 cm
