Sphere
1. Describe the properties of the sphere and its parts:
- sphere
- spherical layer (shell)
- spherical segment
- spherical sector
- spherical cap / zone
Sphere
r – radius
d – diameter
Spherical layer
p1, p2 – radii of the cross-sections
v – height of the layer
Spherical segment
r – radius of the sphere
p – radius of the segment
v – height of the segment
Spherical sector
r – radius of the sphere
v – height of the segment
Spherical cap or zone
r = radius of the sphere
v = height of the cap or zone
S = 2π.r.v
2. The table lists values characterizing spheres.
3. Three spheres with radii r1 = 3 cm, r2 = 4 cm, r3 = 5 cm are to be melted and cast into one sphere.
The radius of the new sphere will be R = 6 cm.
4. A cube is inscribed in a sphere with radius r = 6 cm.
5. What is the mass of a hollow brass sphere (ρ = 8.5 g·cm-3) if the outer diameter is D = 12 cm and the wall thickness is h = 2 mm?
Please log in to view the solution.6. A sphere and a cone are inscribed in a right circular cylinder.
7. A planar cross-section of a sphere has length l = 125.6 cm. The distance of the section from the center of the sphere is v = 6 cm.
8. A spherical segment with height v = 5 cm has volume V = 850 cm3.
9. The height of a spherical cap equals one third of the sphere’s radius.
10. Calculate the mass of a biconvex glass lens (ρ = 3.5 g·cm-3) with diameter 10 cm and thickness 1.2 cm.
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