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$The volume of this cone is 156 pim^(3). What is the height (h) ? Write your answer as a whole number, simplified fraction, or exact decimal.$

The volume of this cone is $156 \pi m^{3}$ . $\newline$ What is the height $h$ ? $\newline$ Write your answer as a whole number, simplified fraction, or exact decimal.

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The volume of this cone is

156 \pi m^{3}

.

\newline

What is the height

h

?

\newline

Write your answer as a whole number, simplified fraction, or exact decimal.

Identify Given Values and Formula: Identify the given values and the formula to use. We know the volume of the cone $V$ is $188.6$ cubic units, the radius $R$ is $6$ units, and the formula for the volume of a cone is $V = \frac{1}{3}\pi R^2 h$ .
Substitute Values into Formula: Substitute the known values into the volume formula to solve for h. $\newline$ $188.6 = \frac{1}{3} \times 3.14 \times 6^2 \times h$ $\newline$ $188.6 = \frac{1}{3} \times 3.14 \times 36 \times h$ $\newline$ $188.6 = 37.68h$
Isolate and Solve for h: Isolate h by dividing both sides of the equation by $37$ . $68$ . $\newline$ $h = \frac{188.6}{37.68}$ $\newline$ $h = 5.01$

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