Final answer:
To find the height and volume of the cylinder, first calculate the radius using the circumference formula. Then, use the curved surface area formula to find the height. Finally, calculate the volume using the volume formula of a cylinder is 15,537 cm³.
Step-by-step explanation:
To find the height and volume of the cylinder, we can use the given information:
The curved surface area of the cylinder is 5,500 cm², and the circumference of the base is 110 cm.
First, let's calculate the radius of the base using the formula for the circumference of a circle:
C = 2πr
110 cm = 2πr
Dividing both sides by 2π, we get:
r ≈ 17.53 cm
Now, we can calculate the height of the cylinder using the formula for the curved surface area:
CSA = 2πrh
5,500 cm² = 2π(17.53 cm)h
Dividing both sides by 2π(17.53 cm), we get:
h ≈ 15.79 cm
Finally, we can calculate the volume of the cylinder using the formula:
V = πr²h
V ≈ 3.142 × (17.53 cm)² × 15.79 cm ≈ 15,537 cm³