Cylinder — Grade 8 Math, what it means and where it is taught
Two parallel circles joined by a curved surface. V = π r2 h.
Taught in Grade 8 Math.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- π — The circumference of any circle divided by its diameter — about 3.14159.
Practise this idea
23 questions in the course bank use Cylinder, in Plane Sections of 3-D Figures, Volume & Surface Area of 3-D Figures, Volume of Cylinders, Cones & Spheres, Solids: Volume, Sections & Rotations. The first 8 are below; the rest are in those units.
Problem 1
A cylinder is sliced parallel to its base. What shape is the cross section?
- A rectangle
- A circle
- An oval
- A triangle
Worked answer
A circle
A circle, the same size as the base.
Problem 2
A cylinder is sliced straight down through its central axis. What shape appears?
- A circle
- A rectangle
- A triangle
- An oval
Worked answer
A rectangle
A rectangle: as tall as the cylinder and as wide as the diameter.
Problem 3
A cylinder has radius 4 cm and height 10 cm. It is cut vertically through its axis. Find the area of the cross section.
Worked answer
80
Height = 10 cm
Width = 2 × 4 = 8 cm
Area = 10 × 8 = 80 cm2
Problem 4
Find the volume of a cylinder with radius 2 and height 5. Use π ≈ 3.14.
Worked answer
62.8
π r2 = 3.14 × 4 = 12.56
12.56 × 5 = 62.8
Problem 5
A cylinder has radius 3 and height 8. Find its volume in terms of π (enter just the number in front of π).
Worked answer
72
9 × 8 = 72
V = 72π
Problem 6
A cylinder has radius 3 and height 8. Find its surface area in terms of π (enter just the number in front of π).
Worked answer
66
Two circles: 2π(9) = 18π
Label: 2π(3)(8) = 48π
18 + 48 = 66, so SA = 66π
Problem 7
A cone and a cylinder have the same base and height. The cone holds what fraction of the cylinder?
- 12
- 13
- 23
- 14
Worked answer
13
Vcone = 13Bh, so it holds one third.
Problem 8
A cylinder has volume 100π and radius 5. Find its height.
Worked answer
4
25π h = 100π
h = 4