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Molly built a teepee in the shape of a cone. The diameter of the base is $12$ feet and the height is $18$ feet. What is the volume of the cone? $\newline$ A $72\pi \, \text{cu ft}$ $\newline$ B $216\pi \, \text{cu ft}$ $\newline$ C $648\pi \, \text{cu ft}$ $\newline$ D $864\pi \, \text{cu ft}$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. Molly built a teepee in the shape of a cone. The diameter of the base is

12

feet and the height is

18

feet. What is the volume of the cone?

\newline

A

72\pi \, \text{cu ft}

\newline

B

216\pi \, \text{cu ft}

\newline

C

648\pi \, \text{cu ft}

\newline

D

864\pi \, \text{cu ft}

Identify radius of base: Step $1$ : Identify the radius of the base of the cone. $\newline$ Since the diameter of the base is $12$ feet, the radius is half of the diameter. $\newline$ Radius = Diameter / $2$ = $12$ feet / $2$ = $6$ feet.
Use volume formula: Step $2$ : Use the formula for the volume of a cone. $\newline$ The formula for the volume of a cone is $(\frac{1}{3})\pi r^2 h$ , where $r$ is the radius and $h$ is the height. $\newline$ Volume = $(\frac{1}{3})\pi(6 \text{ feet})^2(18 \text{ feet})$ .
Calculate radius squared: Step $3$ : Calculate the square of the radius. $\newline$ Radius squared = $6 \text{ feet} \times 6 \text{ feet} = 36 \text{ square feet}.$
Substitute values and simplify: Step $4$ : Substitute the values into the formula and simplify. $\newline$ Volume = $(\frac{1}{3})\pi(36 \text{ square feet})(18 \text{ feet}) = (\frac{1}{3})\pi(648 \text{ cubic feet}) = 216\pi \text{ cubic feet}$ .

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