Question

A teepee is in the shape of a cone that is 452.16 cubic feet in volume and has a radius of 6 feet. What is the height of the teepee?

Use 3.14 for π.

Step 1: substitute known values into the formula for volume

V = (1/2)Bh

V = (1/3)pi r² h which is the same as V = pi r² h ÷ 3

452.16 = *blank 1* ● *blank 2*² ● *blank 3* ÷ *blank 4*

Options for blank 3

A d
B h
C r
D pi

Answer 1

To fill in the blanks in the equation for the volume of the cone (teepee), we will start with the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

We are given:
- \( V = 452.16 \) cubic feet
- \( r = 6 \) feet
- \( \pi = 3.14 \)

Substituting these values into the volume formula, we get:

\[
452.16 = \frac{1}{3} \cdot 3.14 \cdot (6)^2 \cdot h
\]

Now, calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substituting this value back into the equation:

\[
452.16 = \frac{1}{3} \cdot 3.14 \cdot 36 \cdot h
\]

The equation can be rewritten in a way that matches the format provided in the question:

\[
452.16 = \frac{3.14 \cdot 36}{3} \cdot h
\]

Now, we can evaluate \( \frac{3.14 \cdot 36}{3} \):

First, calculate \( 3.14 \cdot 36 \):

\[
3.14 \cdot 36 = 113.04
\]

Now divide by 3:

\[
\frac{113.04}{3} = 37.68
\]

So, we can rewrite our volume equation as:

\[
452.16 = 37.68 \cdot h
\]

Now we compare this with the format given in the question, which is:

\[
452.16 = *blank 1* \cdot *blank 2*^2 \cdot *blank 3* \div *blank 4*
\]

From our calculations, we can see that:

- Blank 1: \( \frac{1}{3} \) (expressed as a fraction)
- Blank 2: \( r = 6 \)
- Blank 3: \( h \)
- Blank 4: \( 3 \)

Now referring to the options provided for blank 3, which includes:

A. d
B. h
C. r
D. pi

The correct option for blank 3 is **B. h**.

Thus, the final filled-in equation is:

\[
452.16 = \frac{1}{3} \cdot 3.14 \cdot 6^2 \cdot h \div 3
\] where \( \text{blank 3 is } h\).