Spherical cap - area and volume
A = π. (q2 + 2.r.h)
V = 1/3.π.h2.(3r – h)
A = Area
V = volume
q = basement radius
r = radius
h = height
WHAT IS IT ?
A spherical cap is a portion of a sphere that is cut off by a plane. The properties of a spherical cap include:
- Radius (r): The radius of the sphere from which the cap is derived.
- Height (h): The perpendicular distance from the base of the cap (the circular cross-section) to the top of the cap.
Spherical caps are commonly found in various applications in mathematics, engineering, and design, especially in the construction of domes and other curved structures.
CALCULATION:
EXAMPLE:
The radius of the sphere is 5 cm. The height of the spherical cap is 2 cm and the radius of the base of the cap is 3 cm. What is the area and volume of the spherical cap?
Surface area:
Using the formula A = 2πrv + πq², we substitute the values:
A = 2 * 3.14 * 5 * 2 + 3.14 * 3²;
A = 6.28 * 10 + 3.14 * 9;
A = 62.8 + 28.26
A = 91.06 cm²
Volume:
Using the formula V = πv / 6 * (3ρ² + v²), we substitute the values:
V = ((3.14 * 2) / 6) * (3 * 3² + 2²);
V = (6.28 / 6) * (3 * 9 + 4);
V = 1.04666 * 31
V = 32.46 cm³
