Calculation of Volume of Cylinder with Given Surface Area and Height

Given:
- Surface area of cylinder = 220 cm²
- Height of cylinder = 6.5 cm

Formula to Calculate Volume of Cylinder

The formula to calculate the volume of a cylinder is:

V = πr²h

where V is the volume, r is the radius of the base, and h is the height of the cylinder.

Calculation of Radius of Cylinder

We can calculate the radius of the cylinder using the formula for the surface area of a cylinder:

A = 2πrh + 2πr²

where A is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

220 = 2πr(6.5) + 2πr²

Simplifying the equation, we get:

110 = πr(6.5 + r)

Dividing both sides by π, we get:

35.026 = r(6.5 + r)

Using the quadratic formula, we get:

r = 4.04 cm or -10.54 cm

Since radius cannot be negative, we take r = 4.04 cm.

Calculation of Volume of Cylinder

Now that we have the radius, we can use the formula for the volume of a cylinder to find the volume:

V = πr²h

Substituting the given values, we get:

V = π(4.04)²(6.5)

V = 532.67 cm³

Therefore, the volume of the cylinder is 532.67 cm³.