If the lateral surface a cylinder is 94.2 cm 2 and its height is 5 cm, then findI. Radius of its base andII. Its volume

To solve this question, we will use the formulas for the lateral surface area and volume of a cylinder.

Given:
Lateral surface area of the cylinder = 94.2 cm²
Height of the cylinder (h) = 5 cm
Step 1: Find the radius of the base of the cylinder
The formula for the lateral surface area of a cylinder is: Lateral surface area = 2 * π * r * h

Where:

r is the radius of the base
h is the height of the cylinder
Substitute the known values into the formula: 94.2 = 2 * π * r * 5

Now, solve for r: 94.2 = 10 * π * r r = 94.2 / (10 * π)

Using the approximate value of π (π ≈ 3.14): r = 94.2 / (10 * 3.14) r = 94.2 / 31.4 r ≈ 3 cm

So, the radius of the base is approximately 3 cm.

Step 2: Find the volume of the cylinder
The formula for the volume of a cylinder is: Volume = π * r² * h

Substitute the values of r and h: Volume = 3.14 * (3)² * 5 Volume = 3.14 * 9 * 5 Volume = 3.14 * 45 Volume ≈ 141.3 cm³

Final Answers:
The radius of the base is approximately 3 cm.
The volume of the cylinder is approximately 141.3 cm³.