The volume of a cone is `1570 cm^(3)` and its height is 15 cm. What is the radius of the cone ? (Use `pi = 3.14`)

Options

A. 10 cm
B. 9 cm
C. 12 cm
D. 8.5 cm

Explanation

To find the radius of the cone given its volume and height, we can use the formula for the volume of a cone:

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

Where:
- \( V \) is the volume of the cone,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is a constant approximately equal to 3.14.

Given:
- Volume \( V = 1570 \, cm^3 \)
- Height \( h = 15 \, cm \)
- \( \pi = 3.14 \)

### Step 1: Substitute the known values into the volume formula.

\[ 1570 = \frac{1}{3} \times 3.14 \times r^2 \times 15 \]

### Step 2: Simplify the equation.

Multiply both sides by 3 to eliminate the fraction:

\[ 3 \times 1570 = 3.14 \times r^2 \times 15 \]

This gives:

\[ 4710 = 3.14 \times r^2 \times 15 \]

### Step 3: Divide both sides by 15.

\[ \frac{4710}{15} = 3.14 \times r^2 \]

Calculating the left side:

\[ 314 = 3.14 \times r^2 \]

### Step 4: Divide both sides by 3.14.

\[ r^2 = \frac{314}{3.14} \]

Calculating the right side:

\[ r^2 = 100 \]

### Step 5: Take the square root of both sides to find \( r \).

\[ r = \sqrt{100} \]

Thus,

\[ r = 10 \, cm \]

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

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