Answer:
6.32 cm.
Step-by-step explanation:
We can see that the given glass is in form of a cone.
To find the height of liquid in glass we will use formula:
[tex]h=\sqrt{l^2-r^2}[/tex], where,
h= Height of cone.
l= Slant height of cone.
r= Radius of cone.
We can see from our figure that diameter of cone is 6 cm, so radius of cone will be half of 6 cm, that is 3 cm.
We have been given slant height equals to 7 cm.
Let us substitute our values in above formula to find the height of liquid in the glass.
[tex]\text{Height of liquid in the glass}=\sqrt{7^2-3^2}[/tex]
[tex]\text{Height of liquid in the glass}=\sqrt{49-9}[/tex]
[tex]\text{Height of liquid in the glass}=\sqrt{40}[/tex]
[tex]\text{Height of liquid in the glass}=6.3245553203367587\approx 6.32[/tex]
Therefore, the height of liquid in the glass is 6.32 cm.
