The height of a cone is 15 cm. If its volume is 1570 `cm^(3)`, find the radius of the base.
(Use `pi=3.14`.)

Answer

To find the radius of the base of the cone given its height and volume, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the formula for the volume of a cone**:
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base, \( h \) is the height, and \( \pi \) is a constant approximately equal to 3.14.

2. **Substitute the known values into the formula**:
We know the volume \( V = 1570 \, \text{cm}^3 \) and the height \( h = 15 \, \text{cm} \). Substituting these values into the formula, we have:
\[ 1570 = \frac{1}{3} \times 3.14 \times r^2 \times 15 \]

3. **Simplify the equation**:
First, calculate \( \frac{1}{3} \times 15 \):
\[ \frac{1}{3} \times 15 = 5 \]
Now, the equation becomes:
\[ 1570 = 5 \times 3.14 \times r^2 \]

4. **Calculate \( 5 \times 3.14 \)**:
\[ 5 \times 3.14 = 15.7 \]
Thus, the equation simplifies to:
\[ 1570 = 15.7 \times r^2 \]

5. **Isolate \( r^2 \)**:
To isolate \( r^2 \), divide both sides by 15.7:
\[ r^2 = \frac{1570}{15.7} \]

6. **Calculate \( \frac{1570}{15.7} \)**:
Performing the division:
\[ r^2 = 100 \]

7. **Find \( r \)**:
To find the radius \( r \), take the square root of \( r^2 \):
\[ r = \sqrt{100} = 10 \, \text{cm} \]

### Final Answer:
The radius of the base of the cone is \( 10 \, \text{cm} \).

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