Which of the following best describes a cone?

A circular base that tapers to a point

All faces are congruent squares

What is a net of a 3D shape?

A two-dimensional pattern that can be folded to form the 3D shape

The set of all vertices of the shape

When a sphere and a cube have the same volume, which statement is true about their surface areas?

The sphere has a smaller surface area

The cube has a smaller surface area

Surface area cannot be determined from volume alone

3D Shapes Quiz - Free Geometry Practice

This quiz helps you practice identifying and comparing 3D shapes through 20 quick questions. You will spot and name solids like cubes, cones, cylinders, and spheres, then see instant results to target what to review next. For more geometry basics, try points lines and planes practice, build measurement skills with the area quiz, or challenge yourself with a broader geometry quiz.

Master faces, edges & vertices - Dive into the building blocks of 3D shapes by counting faces, edges, and vertices. A cube, for instance, has 6 faces, 12 edges, and 8 vertices, which helps you spot patterns across other solids. Understanding these basics is like learning the alphabet before writing epic geometric stories!
Memorize surface area & volume formulas - Lock down key formulas like V = πr²h for cylinders or SA = 6a² for cubes so you can tackle any calculation at lightning speed. These equations are your secret codes to unlock the full potential of every shape. Practice them until they're as natural as breathing!
Navigate the 3D coordinate system - Picture yourself mapping points as (x, y, z) coordinates in space, just like a video game world. This system is your GPS for locating and describing any position in 3D. Mastering it makes visualizing spatial relationships a total breeze!
Use the 3D distance formula - Calculate the straight-line gap between two points using d = √((x₂−x₝)² + (y₂−y₝)² + (z₂−z₝)²). It's like measuring the shortest laser beam in space! With this tool, you'll conquer problems involving lengths in any corner of the coordinate cube.
Decode lines & planes equations - Get comfy with vector and Cartesian forms such as r = a + λb for lines, or ax + by + cz + d = 0 for planes. These equations are your backstage passes to describe any line or flat surface in space. Once you can juggle them, solving intersection and angle problems feels like child's play!
Explore prisms & pyramids - Discover how prisms and pyramids differ by counting faces, edges, and vertices - like knowing a triangular prism has 5 faces, 9 edges, and 6 vertices. Each solid has its own flavor, from a rectangular prism to a pentagonal pyramid. Familiarity here helps you spot similarities and contrasts across polyhedra!
Crunch cones & spheres formulas - Tackle the surface area of a sphere (4πr²) or the volume of a cone (¹❄₃πr²h) like a geometry wizard. These classic shapes show up everywhere, so mastering their formulas gives you an edge in exams and real‑world problems. A little practice, and you'll be unstoppable!
Visualize with nets - Unfold 3D solids into 2D nets to see every face laid out flat - like turning a cardboard box inside out. This trick helps you predict shapes, calculate areas, and even craft models by hand. It's a fantastic way to bridge the gap between flat drawings and real objects!
Calculate angles between lines & planes - Learn how to find the angle between a line and a plane or between two planes using dot products and normal vectors. It's like determining the tilt of a ramp or roof in a design blueprint. Mastering these concepts gives you superpowers in spatial reasoning!
Relate 3D shapes to 2D profiles - Compare solids to their 2D cross‑sections - like linking a cylinder to a circle or a cone to a triangle slice. These relationships reinforce how dimensions build on each other and simplify complex problems. Once you see the pattern, everything clicks into place!