4 Calculate the perpendicular height of a cone that has a base radius 5 cm and a volume of $$ 615 \mathrm{~cm}^{3} $$.

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To calculate the perpendicular height of a cone, 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.

Given:
- The base radius of the cone is 5 cm.
- The volume of the cone is $$ 615 \mathrm{~cm}^{3} $$.

We can substitute the given values into the formula and solve for the height of the cone.
Solve the equation by following steps:
- step0: Solve for $$h$$:
  $$\frac{1}{3}\pi r^{2}h=615$$
- step1: Multiply:
  $$\frac{\pi }{3}r^{2}h=615$$
- step2: Divide both sides:
  $$\frac{\frac{\pi }{3}r^{2}h}{\frac{\pi }{3}r^{2}}=\frac{615}{\frac{\pi }{3}r^{2}}$$
- step3: Divide the numbers:
  $$h=\frac{1845}{\pi r^{2}}$$
The perpendicular height of the cone can be calculated using the formula:

$$ h = \frac{1845}{\pi r^2} $$

Substitute the given values into the formula to find the height of the cone.
The perpendicular height of the cone is $$ \frac{1845}{\pi \times 5^2} $$ cm.

4 Calculate the perpendicular height of a cone that has a base radius 5 cm and a volume of .

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