Cylinder Volume Calculator
Enter the radius and height of a cylinder to find its volume and surface area with full step-by-step work. You can also enter the diameter instead of the radius.
Solution
Cylinder Formulas
A cylinder is a three-dimensional shape with two circular ends (bases) and a curved side. It is defined by its radius ($r$) and height ($h$).
$$\text{Volume} = \pi r^2 h$$ $$\text{Lateral Surface Area} = 2\pi r h$$ $$\text{Total Surface Area} = 2\pi r h + 2\pi r^2$$The lateral surface area is just the curved side — imagine peeling the label off a can. The total surface area adds both circular ends.
Step-by-Step Example
A cylinder has radius $r = 3$ and height $h = 7$.
Volume:
$$V = \pi r^2 h = \pi \times 3^2 \times 7 = \pi \times 9 \times 7 = 63\pi \approx 197.92\ \text{cubic units}$$Lateral Surface Area:
$$LSA = 2\pi r h = 2\pi \times 3 \times 7 = 42\pi \approx 131.95\ \text{sq. units}$$Total Surface Area:
$$TSA = 2\pi r h + 2\pi r^2 = 42\pi + 2\pi \times 9 = 42\pi + 18\pi = 60\pi \approx 188.50\ \text{sq. units}$$Real-World Examples
- A soup can with a radius of 4 cm and height of 10 cm has a volume of $\pi \times 16 \times 10 = 160\pi \approx 502.65\ \text{cm}^3$
- A water tank with a radius of 2 m and height of 5 m holds $\pi \times 4 \times 5 = 20\pi \approx 62.83\ \text{m}^3$ of water
Frequently Asked Questions
What is the difference between volume and surface area?
Volume is the amount of space inside the cylinder — think of how much liquid it can hold. Surface area is the total area of all the outer surfaces — think of how much material you'd need to wrap it.
What if I only have the diameter?
Divide the diameter by 2 to get the radius: $r = d \div 2$. Enter the diameter in the field above and the calculator will convert it automatically.
What are cubic units?
Volume is measured in cubic units — if you measure in inches, volume is in cubic inches (in³). If you measure in centimeters, volume is in cubic centimeters (cm³).
