If $$ v=\frac{1}{3} \pi r^{2} h $$, find $$ v $$ when $$ \pi=\frac{22}{7} $$ $$ r=7 $$ and $$ h=6 $$.

Question

UpStudy AI · Accepted Answer

We are given  
$$
v = \frac{1}{3} \pi r^2 h
$$  
with  
$$
\pi = \frac{22}{7}, \quad r = 7, \quad h = 6.
$$

**Step 1:** Substitute the given values into the formula  
$$
v = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times 6.
$$

**Step 2:** Calculate $$7^2$$  
$$
7^2 = 49.
$$

So,  
$$
v = \frac{1}{3} \times \frac{22}{7} \times 49 \times 6.
$$

**Step 3:** Simplify $$\frac{22}{7} \times 49$$  
$$
\frac{22}{7} \times 49 = 22 \times 7 = 154.
$$

Thus,  
$$
v = \frac{1}{3} \times 154 \times 6.
$$

**Step 4:** Multiply 154 by 6  
$$
154 \times 6 = 924.
$$

Now,  
$$
v = \frac{1}{3} \times 924.
$$

**Step 5:** Divide 924 by 3  
$$
\frac{924}{3} = 308.
$$

**Final Answer:**  
$$
v = 308.
$$
$$ v = 308 $$

If \( v=\frac{1}{3} \pi r^{2} h \), find \( v \) when \( \pi=\frac{22}{7} \) \( r=7 \) and \( h=6 \).