Polyhedra and solids of revolution
Answers are for parents and teachers.
1
A rectangular parallelepiped has dimensions 2, 3 and 6 cm. What is the sum of the lengths of all its edges, in cm?
44
2
A regular pyramid has a square base of side 12 cm and apothem 10 cm. What is its lateral surface in cm²?
240
3
A cylinder has base radius 2 cm and height 7 cm. Find its total surface.
2π · 2 · 7 + 2π · 4 = 28π + 8π = 36π cm².
4
A cone has base radius 4 cm and height 3 cm. Find its generator and lateral surface.
l = √(16 + 9) = 5 cm; S = π · 4 · 5 = 20π cm².
5
A sphere has area 100π cm². Find its radius.
4πr² = 100π ⇒ r² = 25 ⇒ r = 5 cm.