Question

Th e formula for the volume of a cylinder is V = πr 2 h, where r is the radius of the circular base and h is the height of the cylinder.

a. Solve the formula for h.

Answer 1

To solve the formula V = πr^{2}h for h, you divide both sides by πr^{2}, yielding h = V / (πr^{2}). For example, given a cylinder with V = 9.278 cm³ and r = 0.750 cm, h is calculated to be about 5.25 cm.

Step-by-step explanation:

The student asked to solve the formula for the volume of a cylinder, V = πr^{2}h, for the height (h). The formula for the volume of a cylinder can be rearranged to solve for h by dividing both sides by πr^{2}, leading to the solution h = V / (πr^{2}).

For example, if you are given a cylinder with a volume (V) of 9.278 cm³ and a radius (r) of 0.750 cm, the height (h) can be calculated as follows:

1. Identify the given values: V = 9.278 cm³ and r = 0.750 cm.
2. Plug these values into the rearranged formula: h = V / (πr^{2}).
3. Calculate the height: h = 9.278 cm³ / (π × (0.750 cm)^{2}) = 9.278 cm³ / (3.142 × 0.5625 cm²) = 9.278 cm³ / 1.767 cm² ≈ 5.25 cm.

This process demonstrates how to solve for the height of a cylinder when given its volume and the radius of its base.