Cone — Grade 8 Math, what it means and where it is taught
A circle tapering to a point. V = 13π 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.
What uses it later
This idea is needed for:
- Conic section — A curve obtained by slicing a cone with a plane.
Practise this idea
12 questions in the course bank use Cone, 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 cone is sliced parallel to its base. What shape is the cross section?
- A triangle
- A circle
- A trapezoid
- An oval
Worked answer
A circle
A circle — smaller the closer you cut to the tip.
Problem 2
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 3
Find the volume of a cone with r = 3 and h = 4, in terms of π.
Worked answer
12pi
13π(9)(4)
= 12π
Problem 4
Find the volume of a cone with r = 6 and h = 10, in terms of π.
Worked answer
120pi
13π(36)(10)
= 360π3 = 120π
Problem 5
A cone and a cylinder have the same radius and height. The cone's volume is
- one third of the cylinder's
- the same
- twice as much
- three times as much
Worked answer
one third of the cylinder's
Cylinder: π r2 h
Cone: 13π r2 h
So one third
Problem 6
A cone with radius 3 has volume 30π. Find its height.
Worked answer
10
13π(9)h = 30π
3h = 30
h = 10
Problem 7
A silo is a cylinder of radius 3 and height 10 topped by a cone of the same radius and height 4. Find the total volume in terms of π.
Worked answer
102pi
Cylinder: π(9)(10) = 90π
Cone: 13π(9)(4) = 12π
90π + 12π = 102π
Problem 8
Find the volume of a cone with r = 6 and h = 10, in terms of π.
Worked answer
120pi
13 π (36)(10) = 120π