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26 Part I: Technical Mathematics
Examples of Surface Area Calculations
Part I.C
A square prism has length, width, and height equal to 23 cm, 12 cm,
and 30 cm, respectively. Its surface area is 2 × [(23 cm × 12 cm) + (12 cm ×
30 cm) + (23 cm × 30 cm)] = 2 × (276 cm 2 + 360 cm 2 + 690 cm 2 ) = 2652 cm 2 .
A cube has sides of length 13 inches. Its surface area is then 6 × (13 in) 2
= (6 × 13 in × 13 in) = 1014 in 2 .
A cylinder has a radius of 120 mm and a height of 250 mm. Its surface
area is 2 × p × (120 mm) 2 + (2 × p × 120 mm × 250 mm) = 278,973.4 mm 2 .
Note: since the formula involves pi (p), when at all possible use a
calculator to find the surface area of a cylinder to avoid round-off errors.
A cone has a radius of 3.5 inches and a height of 12 inches. Its surface
area is
2 2 2
2
p × ( 35 . in) + p ×( 35 . in)× ( 35 . in) + ( 12in) = 175. 93 in .
Note: since the formula involves pi (p), when at all possible use a calculator
to find the surface area of a cone to avoid round-off errors.
A sphere has a radius equal to 2.05 cm. Its surface area is 4 × p ×
(2.05 cm) 2 = 52.81 cm 2 . Note: since the formula involves pi (p), when at
all possible use a calculator to find the surface area of a sphere to avoid
round-off errors.
COMPLEMENTARY AND SUPPLEMENTARY ANGLES
Two angles that add up to 90°, or a right angle, are called complementary angles. For
example, the angles 30° and 60° are complementary angles.
Two angles that add up to 180°, which is a straight line, are called supplementary
angles. For example, the angles 45° and 135° are supplementary angles.