🧊

3D Shape Surface Area & Volume Calculator

Calculate volume and surface area for Cylinder, Sphere, Cone, and Rectangular Prism with exact pi multiples and liquid gallon conversions.

Select 3D Geometric Shape

Radius r

Height h

Calculated Results

Volume (Capacity)

502.65 Cu Units

Exact: 160π cubic units

Total Surface Area

351.86 Sq Units

Includes bases and lateral sides

Lateral Curved Area

251.33 Sq Units

Side walls only (2πrh)

Liquid Gallons (if inches)

2.18 US Gallons

231 cubic inches per gallon

Geometric Formula Used

V = πr²h

A = 2πrh + 2πr²

Frequently Asked Questions

What is the volume formula for a cylinder, sphere, and cone?

Cylinder: V = πr²h. Sphere: V = (4/3)πr³. Cone: V = (1/3)πr²h. Notice that a cone has exactly one-third the volume of a cylinder with the same radius and height.

What is the surface area formula for a sphere?

The total surface area of a sphere is: A = 4πr², which is exactly equal to four times the area of its great circle.

How many cubic inches are in a US liquid gallon?

One US liquid gallon equals exactly 231 cubic inches (or approximately 3,785 cubic centimeters / 3.785 liters).

What is lateral surface area versus total surface area?

Lateral surface area accounts only for the vertical curved side surfaces excluding top and bottom end caps. Total surface area includes the lateral sides plus the base caps.