CYLINDER
PROBLEM SOLVING:
1.
Cylindrical Surface – surface generated by a straight
line which moves along a fixed curve, and which
remains parallel to a fixed line not on the curve.
The lateral area of a right cylindrical tank is 48π m2 and its volume
is 72π m3. Find the altitude of the tank.
Solution:
r
LSA = 2πrh
48π = 2πrh
24 = rh
24/r = h ①
h
Cylinder – a solid bounded by a closed cylindrical
surface and two parallel planes cutting all the elements
of the surface.
Bases of the cylinder
Lateral face
V = πr2h
72π = πr2h
72 = r2h
72/r2 = h ②
Equate h of ① and ②:
r = 3m
h = 8m
Altitude
2.
Right Circular Cylinder
r
altitude of the tank
A solid cylinder of radius 10 in. is inscribed in a prism with
equilateral triangular bases. Find the volume of the portion of the
prism that is outside the cylinder if their common height is 100
inches.
Solution:
h
h
2πr
600
s
Oblique Cylinder
r
s
10in.
600
A
A’ h
r
Vcylinder = Bh
= πr2h
= π(10)2(100)
= 31 415.93 in3
600
s
apothem = radius = 10 in.
apothem: a=
s
2 tan (180/n)
e
Section AA’
FORMULAS:
Lateral Surface Area:
Total Surface Area:
Volume:
(for oblique):
LSA = 2πrh
TSA = 2πr2 + 2πrh
V = Bh = πr2h
V =Bh = Re
Where R=Bsinθ
s = a (2 tan (180/n))
s = 10(2 tan (180/3))
s = 34.64 in.
Area of triangle given S-A-S
Area of triangle(B)=½ ab sin θ
=½ s2 sin 600
= 519.62 in2
V prism= Bh = (519.6152 in2)(100in)
= 51961.52 in3
Volume required = Vprism – Vcylinder
= 51 961.52in3 - 31 415.93in3
= 20 545.59 in3
CYLINDER
Cylindrical Surface – surface generated by a straight
line which moves along a fixed curve, and which
remains parallel to a fixed line not on the curve.
PROBLEM SOLVING:
1.
The lateral area of a right cylindrical tank is 48π m2 and its volume
is 72π m3. Find the altitude of the tank.
Solution:
Cylinder – a solid bounded by a closed cylindrical
surface and two parallel planes cutting all the elements
of the surface.
Bases of the cylinder
Lateral face
Altitude
Right Circular Cylinder
r
2.
h
h
2πr
FORMULAS:
Lateral Surface Area:
Total Surface Area:
Volume:
(for oblique):
LSA = 2πrh
TSA = 2πr2 + 2πrh
V = Bh = πr2h
V =Bh = Re
Where R=Bsinθ
Oblique Cylinder
r
A
A’
h
r
e
Section AA’
A solid cylinder of radius 10 in. is inscribed in a prism with
equilateral triangular bases. Find the volume of the portion of the
prism that is outside the cylinder if their common height is 100
inches.
Solution:
3.
Find the volume of:
600
5cm
4.
A cylindrical oiler can contain 848 g of machine oil. The
height of the oiler is 12cm. Find the radius of the oiler if
the density of oil is equal to 900 kg/m3.
5.
A closed cylindrical tank 10 ft. in height and 4 ft. in
diameter contains water with depth of 3 ft. and 5 in. What
would be the height of the water when the tank is lying in
a horizontal position?