Panasonic DLP PT-D12000U, Operating Instructions Manual

Page: 169 / 200

SURFACE AREA AND VOLUME CALCULATIONS
Triangle A (area) = ½ x b x h;
where b is the base and h is the height of the triangle
Rectangle A (area) = a x b;
where a and b are the lengths of the sides
Rectangular Box V (volume) = w x l x h;
where w is the width, l is the length, and h is the height
Parallelogram (a 4-sided figure with opposite sides parallel)
A (area) = a x h; or a x b x sin
Q
;
where a and b are the length of the sides, h is the altitude (or
vertical height), and
Q
is the angle between the sides
Trapezoid (a 4-sided figure with two sides parallel)
A (area) = ½ x h (a + b);
where a and b are the length of the sides and h is the height
Regular polygon of n sides
A (area) = 1/4 x n x a x cotangent (180 / n );
2 0
where a is the length of a side and n is the number of sides
Circle A (area) =
p
x r ; or 1/4 x
p
x d ;
2 2
where r is the radius and d is the diameter
Cube A (area) = 6 x a ;
2
V (volume) = a ;
3
where a is the length of a side
Cylinder A (area) = 2 x
p
x r x h;
V (volume) =
p
x r x h;
2
where r is the radius and h is the length of the height
Sphere A (area) = 4 x
p
x r ; or
p
x d ;
2 2
V (volume) = 4/3 x p x r or 1/6 x p x d
3 3
where r is the radius and d is the diameter
158
SURFACE AREA AND VOLUME CALCULATIONS
Triangle A (area) = ½ x b x h;
where b is the base and h is the height of the triangle
Rectangle A (area) = a x b;
where a and b are the lengths of the sides
Rectangular Box V (volume) = w x l x h;
where w is the width, l is the length, and h is the height
Parallelogram (a 4-sided figure with opposite sides parallel)
A (area) = a x h; or a x b x sin
Q
;
where a and b are the length of the sides, h is the altitude (or
vertical height), and
Q
is the angle between the sides
Trapezoid (a 4-sided figure with two sides parallel)
A (area) = ½ x h (a + b);
where a and b are the length of the sides and h is the height
Regular polygon of n sides
A (area) = 1/4 x n x a x cotangent (180 / n );
2 0
where a is the length of a side and n is the number of sides
Circle A (area) =
p
x r ; or 1/4 x
p
x d ;
2 2
where r is the radius and d is the diameter
Cube A (area) = 6 x a ;
2
V (volume) = a ;
3
where a is the length of a side
Cylinder A (area) = 2 x
p
x r x h;
V (volume) =
p
x r x h;
2
where r is the radius and h is the length of the height
Sphere A (area) = 4 x
p
x r ; or
p
x d ;
2 2
V (volume) = 4/3 x
p
x r or 1/6 x
p
x d
3 3
where r is the radius and d is the diameter
158
SURFACE AREA AND VOLUME CALCULATIONS
Triangle A (area) = ½ x b x h;
where b is the base and h is the height of the triangle
Rectangle A (area) = a x b;
where a and b are the lengths of the sides
Rectangular Box V (volume) = w x l x h;
where w is the width, l is the length, and h is the height
Parallelogram (a 4-sided figure with opposite sides parallel)
A (area) = a x h; or a x b x sin
Q
;
where a and b are the length of the sides, h is the altitude (or
vertical height), and
Q
is the angle between the sides
Trapezoid (a 4-sided figure with two sides parallel)
A (area) = ½ x h (a + b);
where a and b are the length of the sides and h is the height
Regular polygon of n sides
A (area) = 1/4 x n x a x cotangent (180 / n );
2 0
where a is the length of a side and n is the number of sides
Circle A (area) =
p
x r ; or 1/4 x
p
x d ;
2 2
where r is the radius and d is the diameter
Cube A (area) = 6 x a ;
2
V (volume) = a ;
3
where a is the length of a side
Cylinder A (area) = 2 x
p
x r x h;
V (volume) =
p
x r x h;
2
where r is the radius and h is the length of the height
Sphere A (area) = 4 x p x r ; or p x d ;
2 2
V (volume) = 4/3 x
p
x r or 1/6 x
p
x d
3 3
where r is the radius and d is the diameter
`
158
SURFACE AREA AND VOLUME CALCULATIONS
Triangle A (area) = ½ x b x h;
where b is the base and h is the height of the triangle
Rectangle A (area) = a x b;
where a and b are the lengths of the sides
Rectangular Box V (volume) = w x l x h;
where w is the width, l is the length, and h is the height
Parallelogram (a 4-sided figure with opposite sides parallel)
A (area) = a x h; or a x b x sin
Q
;
where a and b are the length of the sides, h is the altitude (or
vertical height), and
Q
is the angle between the sides
Trapezoid (a 4-sided figure with two sides parallel)
A (area) = ½ x h (a + b);
where a and b are the length of the sides and h is the height
Regular polygon of n sides
A (area) = 1/4 x n x a x cotangent (180 / n );
2 0
where a is the length of a side and n is the number of sides
Circle A (area) =
p
x r ; or 1/4 x
p
x d ;
2 2
where r is the radius and d is the diameter
Cube A (area) = 6 x a ;
2
V (volume) = a ;
3
where a is the length of a side
Cylinder A (area) = 2 x
p
x r x h;
V (volume) =
p
x r x h;
2
where r is the radius and h is the length of the height
Sphere A (area) = 4 x
p
x r ; or
p
x d ;
2 2
V (volume) = 4/3 x
p
x r or 1/6 x
p
x d
3 3
where r is the radius and d is the diameter
158