SOLUTION: A vessel has a shape of a right circular cone with a depth of 33 cm and a top diameter 22 cm. The vessel contains liquid to a depth of 15 cm. How many more litres of liquid needs t

Algebra ->  Volume -> SOLUTION: A vessel has a shape of a right circular cone with a depth of 33 cm and a top diameter 22 cm. The vessel contains liquid to a depth of 15 cm. How many more litres of liquid needs t      Log On


   

Question 1154329: A vessel has a shape of a right circular cone with a depth of 33 cm and a top diameter 22 cm. The vessel contains liquid to a depth of 15 cm. How many more litres of liquid needs to be added in order to fill the vessel?
Round to one decimal place.

please help me solve it
thanks
Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The diameter and depth of the cone are in the ratio 22:33 = 2:3.

When the cone is filled to any depth, the liquid is in the shape of a cone similar to the whole cone -- that is, the diameter and depth are always in the ratio 2:3.

So when the depth of the liquid is 15cm, the diameter of the surface of the liquid is 10cm.

The volume of the cone in cm^3 is

%281%2F3%29%28pi%29%2811%5E2%29%2833%29+=+1331pi

When the depth of the liquid is 15cm, the volume of liquid is

%281%2F3%29%28pi%29%285%5E2%29%2815%29+=+125pi

The amount of liquid needed to fill the container is

1331pi-125pi+=+1206pi

Perform the calculation and convert the answer in cm^3 to liters. (1 liter = 1000 cm^3)

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
.
Volume of Frustum of a cone = %28pi%2Ah%2F3%29%28R%5E2%2Br%5E2%2BrR%29
here R =11, r=5, h=18
plug values
(6*pi)*(11^2+5^2+55) =3789 cm^3
1 liter = 1000 cm^3
3,789 liters is required