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:
, 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.
![\text{Height of liquid in the glass}=\sqrt{7^2-3^2}](https://tex.z-dn.net/?f=%5Ctext%7BHeight%20of%20liquid%20in%20the%20glass%7D%3D%5Csqrt%7B7%5E2-3%5E2%7D)
![\text{Height of liquid in the glass}=\sqrt{49-9}](https://tex.z-dn.net/?f=%5Ctext%7BHeight%20of%20liquid%20in%20the%20glass%7D%3D%5Csqrt%7B49-9%7D)
![\text{Height of liquid in the glass}=\sqrt{40}](https://tex.z-dn.net/?f=%5Ctext%7BHeight%20of%20liquid%20in%20the%20glass%7D%3D%5Csqrt%7B40%7D)
![\text{Height of liquid in the glass}=6.3245553203367587\approx 6.32](https://tex.z-dn.net/?f=%5Ctext%7BHeight%20of%20liquid%20in%20the%20glass%7D%3D6.3245553203367587%5Capprox%206.32)
Therefore, the height of liquid in the glass is 6.32 cm.