The cylinder and chapter review
Answers are for parents and teachers.
1
The diagonal of a cylinder’s axial section makes 60° with the base plane, and the base radius is 3. Find the height and the volume.
h = 2r · tan 60° = 6√3; V = π · 9 · 6√3 = 54√3π.
2
A metal part is immersed in a cylindrical vessel (r = 5 cm) and the water rises 3 cm. Find the part’s volume (π ≈ 3.14).
V = π · 25 · 3 = 75π ≈ 235.5 cm³.
3
Find the area of the net of a cylinder with height 10 and base radius 3.
S_total = 2π · 3 · 13 = 78π ≈ 245.
4
Find the volume of the cylinder circumscribed about a regular triangular prism (base side 6, height 8). (The circumradius of an equilateral triangle is a/√3.)
R = 6/√3 = 2√3, R² = 12; V = π · 12 · 8 = 96π.
5
Two cylinders have equal heights and radii 2 and 3. Find the ratio of their volumes.
4 : 9 (the ratio of the squares of the radii).