Volume and surface area of prisms and cylinders
Turn prisms and cylinders, find the base (of a prism, cylinder, pyramid or cone), fill them layer by layer to see why volume = base area × height, and open the net (of a solid) to work out the lateral surface area and the total surface area.
- UK: Year 8
- France: grade 3
- Germany: grade 5
- Iran: grade 7
- Afghanistan: grade 8
- Syria: grade 6
- Palestine: grade 5
- Ukraine: grade 5
- Russia: grade 10
Guide
This studio follows KS3 "volume of cuboids and other prisms, including cylinders" (Iran G7 ch.6, Afghan G8 ch.6). All lengths are in cm, and the cylinder missions take π as 3.14.
Turn the solid by dragging it, with the arrow buttons or with the arrow keys. "Hidden edges" shows the edges at the back as dashed lines. The line under the picture says which faces can be seen from where you are.
The base is the cross-section the prism is made of when you slice it parallel to the ends; it does not have to be at the bottom. A prism lying on its side still has its two triangles as its bases.
Common slips: taking a rectangle as the base, counting only the faces you can see, writing πr²h for a cylinder's curved surface, mixing up cm² and cm³, and adding the edges instead of finding the volume. Each one gets its own feedback.