Question

Water is draining from a tank shaped like a cone.

Answer 1

Answer:

6.0 ft (option C)

Step-by-step explanation:

Given:

The height of the tank = 10 ft

The width of the tank = 25ft

when the with of the tank is 15 ft, the height is unknown

To find:

the height of the water when the length across the water is 15ft

To determine the height, we will apply the similarity theorem:

`\begin{gathered} \frac{height\text{ of the tank}}{height\text{ 15 ft wideness}}\text{ = }\frac{width\text{ of tank}}{15ft\text{ wideness}} \\ \\ let\text{ height of the 15ft wideness = h} \end{gathered}`
`\begin{gathered} \frac{10\text{ }}{h}\text{ = }(25)/(15) \\ \\ cross\text{ multiply:} \\ 10(15)\text{ = h\lparen25\rparen} \\ 150\text{ = 25h} \end{gathered}`
`\begin{gathered} divide\text{ both sides by 25:} \\ (150)/(25)\text{ = h} \\ \\ h\text{ = 6 } \end{gathered}`

The height of the water when the length across the water is 15ft is 6.0 ft (option C)