SOLUTION: A water tank has the shape of a cone with the vertex down. The tank is 10 m high and has a base radius of 3 m. When the water in the tank is 5 m deep, what is the area of the surfa

Question 893993: A water tank has the shape of a cone with the vertex down. The tank is 10 m high and has a base radius of 3 m. When the water in the tank is 5 m deep, what is the area of the surface of the water at that instant? (Hint: make a sketch and set up similar triangles.)
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Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
This really works better with a picture.
Top diameter for the tank is 3 m, and distance top to bottom of the tank is 10 m.
The ratio of diameter to height, . This is using d for DIAMETER and h for HEIGHT or DEPTH. You can recognize similar triangles if this helps.

If you want the surface area of the top of the liquid when the filled depth is 5 m, then:

Know that half of diameter is radius; so the radius at that depth is

Now to get the value for this surface area of the liquid at the top of this depth, .
Answer by MathTherapy(10553) (Show Source): You can put this solution on YOUR website!

A water tank has the shape of a cone with the vertex down. The tank is 10 m high and has a base radius of 3 m. When the water in the tank is 5 m deep, what is the area of the surface of the water at that instant? (Hint: make a sketch and set up similar triangles.)

Diameter of circular top of water at the 5m mark of cone = 3 m, or radius of: , or 1.5m
Area of surface of water at the 5m mark: , or , or , or
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