In geometry, a pyramid with a circular base. If the point (vertex) is directly above the centre of the circle, it is known as a
right circular cone. The
volume (
V) of this cone is given by the formula
V = 1/3πr2h where
h is the perpendicular height and
r is the base radius.
A right circular cone is generated by rotating an isosceles triangle about its line of symmetry. The distance from the edge of the base of a cone to the vertex is called the slant height. In a right circular cone of slant height
l, the curved surface area is π
rl, and the area of the base is π
r2. Therefore the total surface area
A = π
rl + π
r2 = π
r(
l +
r).
For example, to find the volume and surface area of a cone with a perpendicular height of 4 cm and radius of 3 cm:
Volume =
1/3π
r2h, so
V = 1/3π × 32 × 4
V = 37.7 cm3 (to 1 decimal place)
Surface area = π
r(
l +
r). First the slant length (
l) is calculated:
Using
Pythagoras' theorem,
l2 = h2 + r2, so
l2 = 42 + 32 = 16 + 9 = 25, so
l = 5 cm
The surface area can now be calculated:
A = πr(l + r), so
A = π × 3(3 + 5) = 3π × 8 = 24π, so
A = 75.4 cm2 (to 1 decimal place)
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