Question 3 The volume of a cone with height $$ h $$ and radius $$ r $$ can be found using the formula $$ V=\frac{1}{3} \pi r^{2} h $$ Find the volume of a cone with radius 9 feet and height 6 feet. Check Answer $$ \mathrm{ft}^{3} $$

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UpStudy AI · Accepted Answer

**Step 1:** Write down the formula for the volume of a cone:

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

**Step 2:** Substitute the given values $$ r = 9 $$ feet and $$ h = 6 $$ feet into the formula:

$$
V = \frac{1}{3} \pi (9)^2 (6)
$$

**Step 3:** Calculate $$ (9)^2 $$:

$$
(9)^2 = 81
$$

Thus, the volume becomes:

$$
V = \frac{1}{3} \pi \cdot 81 \cdot 6
$$

**Step 4:** Multiply $$ 81 $$ by $$ 6 $$:

$$
81 \times 6 = 486
$$

Now, the formula is:

$$
V = \frac{1}{3} \pi \cdot 486
$$

**Step 5:** Divide $$ 486 $$ by $$ 3 $$:

$$
\frac{486}{3} = 162
$$

So the volume is:

$$
V = 162\pi \, \text{ft}^3
$$
The volume of the cone is $$ 162\pi $$ cubic feet.

Question 3 The volume of a cone with height \( h \) and radius \( r \) can be found using the formula \( V=\frac{1}{3} \pi r^{2} h \) Find the volume of a cone with radius 9 feet and height 6 feet. Check Answer \( \mathrm{ft}^{3} \)

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