Question

If the volume of a right circular cylinder is given as 50 cubic centimeters and if its radius measures 2 centimeters, calculate its height.

Short answer

Answer: The height of the right circular cylinder is approximately 3.98 centimeters.

Step-by-step solution

Write down the given information.

We are given the volume V of the right circular cylinder as 50 cubic centimeters (cm³), and its radius r as 2 centimeters (cm).

Write the formula for the volume of a cylinder.

The formula for the volume of a right circular cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

Plug in the given values into the formula.

We have V = 50 cm³, and r = 2 cm. We can substitute these values into the formula: 50 = π(2)²h

Simplify the equation.

We can simplify the equation by performing the exponent and multiplication operations: 50 = 4πh

Solve for the height h.

Divide both sides of the equation by 4π to isolate the variable h: h = \frac{50}{4\pi}

Calculate the height.

Calculate the height of the right circular cylinder: h ≈ \frac{50}{4\pi} ≈ 3.98 cm The height of the right circular cylinder is approximately 3.98 centimeters.