Cone - area and volume
A = πr ( r + s )
V = 1/3 πr2v
A = Area
V = volume
d = diameter
r = radius
h = height
s = slant height
WHAT IS IT ?
A cone is a three-dimensional geometric shape with a circular base and a single vertex, called the apex, that is not in the same plane as the base. The properties of a cone include the height, which is the perpendicular distance from the base to the apex, and the slant height, which is the distance from the apex to any point on the edge of the base. The surface area of a cone consists of the base area and the lateral surface area. The volume of a cone is one-third the product of the base area and the height. Cones are commonly found in various applications in mathematics, architecture, engineering, and everyday objects like ice cream cones and traffic cones.
CALCULATION:
EXAMPLE:
The radius of the cone is, for example, 4 cm. The slant height s is, for example, 6 cm.
Thus
r = 4,
s = 6
area of the cone:
We use the formula
A = πr (r + s)
thus
A = 3.14 * 4 * (4 + 6)
A = 125.66 cm²
volume of the cone:
The radius of the cone is, for example, 4 cm. The height is, for example, 8 cm.
Thus
r = 4,
v = 8
We use the formula
V = 1/3 πr²v
thus
V = 1/3 * 3.14 * 4² * 8
V = 134.04 cm³
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