SOLUTION: A cone of height 48cm is filled to a height of 40cm. If the cone has a diameter of 54cm, find the diameter of the cone at the surface of the water.

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Question 1118091: A cone of height 48cm is filled to a height of 40cm. If the cone has a diameter of 54cm, find the diameter of the cone at the surface of the water.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write and use the proportion


48%2F40 = 54%2Fx,


and obtain the solution  x = %2840%2A54%29%2F48 = 45 centimeters.


Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The shape of the water in the cone is a cone similar to the whole cone.

In similar figures, the ratios of corresponding measurements of length are the same.

This problem involves linear measurements: the height of the whole cone is 48cm; the height of the water in the cone is 40cm; the diameter of the whole cone is 54cm; and we are asked for the diameter of the surface of the water. So

40%2F48+=+x%2F54
5%2F6+=+x%2F54
x+=+45

The diameter of the surface of the water is 45cm.