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Solid Geometric Shapes Summary |
SOLID GEOMETRIC FIGURES
Geometry
Example:
Calculate the volume and surface area of a right circular cone with r = 3", h = 4", and
l = 5". Be sure to include the units in your answer.
Solution:
V = 1/3pr2h
SA = pr2 + prl
V = 1/3p(3)(3)(4)
SA = p(3)(3) + p(3)(5)
V = 1.05(36)
SA = p(9) + p(15)
V = 37.8 cubic inches
SA = 28.3 + 47.1
SA = 528/7 = 75-3/7 square inches
Right Circular Cylinder
Figure 18 Right Circular Cylinder
A right circular cylinder is a cylinder whose base is
perpendicular to its sides. Facility equipment, such as
the reactor vessel, oil storage tanks, and water storage
tanks, is often of this type.
The volume of a right circular cylinder is calculated
using the following formula:
V = pr2h
(3-19)
The surface area of a right circular cylinder is calculated
using the following formula:
SA = 2prh + 2pr2
(3-20)
The surface area of a right circular cylinder is expressed in square units, and the volume of a
right circular cylinder is expressed in cubic units.
Example:
Calculate the volume and surface area of a right circular cylinder with r = 3" and
h = 4". Be sure to include units in your answer.
Solution:
V = pr2h
SA = 2prh + 2pr2
V = p(3)(3)(4)
SA = 2p(3)(4) + 2p(3)(3)
V = p(36)
SA = 2p(12) + 2p(9)
V = 113.1 cubic inches
SA = 132 square inches
MA-03
Page 16
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