Question

A closed container in the form of an inverted right ˚ular cone has a base radius of 14 ft, altitude of 15 ft, and contains water 10 ft deep. Find the height of the water when the container is turned upside down (base at the bottom).

a) 3 ft
b) 5 ft
c) 7 ft
d) 10 ft

Answer 1

To find the height of the water when the container is turned upside down, we can use the concept of similar triangles. The height of the water when the container is upright is 10 ft. When the container is turned upside down, the water will form a cone with a smaller height but the same shape as the original cone. Using a proportion, we can solve for the height of the water in the upside down position, which is 5 ft.

Step-by-step explanation:

To find the height of the water when the container is turned upside down, we can use the concept of similar triangles. The height of the water when the container is upright is 10 ft. When the container is turned upside down, the water will form a cone with a smaller height but the same shape as the original cone. Let's call the height of the water in the upside down position h. We can set up a proportion:

h/10 = (14+h)/15

Solving this proportion, we find h = 5 ft. Therefore, the height of the water when the container is turned upside down is 5 ft.