Pyramid — Geometry, what it means and where it is taught
A base tapering to a point. V = 13 Bh.
Taught in Geometry.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Base — The number being multiplied. In 53 the base is 5.
Practise this idea
6 questions in the course bank use Pyramid, in Plane Sections of 3-D Figures, Solids: Volume, Sections & Rotations, Surface Area & Nets.
Problem 1
A square pyramid is sliced parallel to its base. What shape is the cross section?
- A triangle
- A square
- A trapezoid
- A pentagon
Worked answer
A square
A square — smaller the higher up you cut.
Problem 2
A square pyramid is sliced vertically through its apex. What shape appears?
- A square
- A trapezoid
- A triangle
- A circle
Worked answer
A triangle
A triangle, with the apex at the top of the cut.
Problem 3
A pyramid has base area 30 and height 12. Find its volume.
Worked answer
120
13 (30)(12) = 120
Problem 4
How many faces does a square pyramid have?
Worked answer
5
One square and four triangles
Problem 5
A square pyramid has base edge 6 and slant height 5. Find its surface area.
Worked answer
96
36 + 4(15) = 96
Problem 6
A square pyramid has base edge 10 and slant height 12. Find its surface area.
Worked answer
340
100 + 4(60) = 340