Volume & Surface Area Worksheet
Goal: Find the volume and surface area of prisms, cylinders, cones and spheres, and discover how the shapes and their dimensions are related.
What to do
- Open the volume calculator. Keep “Length unit” on centimeters.
- For each solid in the table, choose it in “Shape”, enter its dimensions and record the volume and surface area.
- Before answering the questions, compare rows that share a radius or a height and look for patterns.
Record your results
| Setting | Volume | Surface area |
|---|---|---|
| Rectangular prism: 6 × 4 × 3 | ||
| Cylinder: radius 3, height 8 | ||
| Cone: radius 3, height 8 | ||
| Cylinder: radius 6, height 8 | ||
| Sphere: radius 5 | ||
| Cylinder: radius 5, height 10 | ||
| Rectangular prism: 6 × 6 × 8 |
Questions
Find the volume and surface area of the 6 × 4 × 3 prism by hand.
The cone and the first cylinder have the same radius and height. How do their volumes compare?
When the cylinder’s radius doubled from 3 to 6 (same height), by what factor did the volume grow? Why?
The sphere with radius 5 fits exactly inside the cylinder with radius 5 and height 10. What fraction of the cylinder does the sphere fill?
Find the sphere’s volume by hand with V = ⁴⁄₃πr³.
A juice company can sell its juice in a cylinder (radius 3 cm, height 8 cm) or a box (6 cm × 6 cm × 8 cm). Which holds more, and which needs more packaging material?
Free from Geometry Lab · geometrylab.net · 7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects. 8.G.C.9: Know the formulas for the volumes of cones, cylinders and spheres and use them to solve problems.
Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.