Find the redius of a cone whose height is 5cm and volume is 115cm?

To find the radius of a cone, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

where V is the volume, r is the radius, h is the height, and π is a constant approximately equal to 3.14159.

Given that the height is 5 cm and the volume is 115 cm^3, we can plug these values into the formula and solve for the radius:

115 = (1/3) * π * r^2 * 5
115 = (π/3) * 5r^2
r^2 = 115 / (5 * π/3)
r^2 = 69 / π
r ≈ √(69 / π)
r ≈ √(69 / 3.14159)
r ≈ √21.95
r ≈ 4.68 cm

Therefore, the radius of the cone is approximately 4.68 cm.

Given:

- Height of the cone (h) = 5 cm
- Volume of the cone (V) = 115 cm³

Formula:

The volume of a cone is given by:

```
V = (1/3) - π - r² - h
```

where:

- V is the volume of the cone
- r is the radius of the cone
- h is the height of the cone
- π is a mathematical constant approximately equal to 3.14

Solution:

Substituting the given values into the formula, we get:

```
115 cm³ = (1/3) - π - r² - 5 cm
```

Rewriting for r:

```
r² = (115 cm³ - 3) / (π - 5 cm)
```

```
r² = (345 cm³) / (5 cm - 3.14)
```

```
r² = 21.88 cm²
```

Taking the square root of both sides:

```
r = √21.88 cm²
```

```
r = 4.68 cm (rounded to two decimal places)
```

Therefore, the radius of the cone is 4.68 cm.