a prism is a solid whose sides (lateral sides) are parallelograms and whose bases are a pair of...
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A prism is a solid whose sides (lateral sides) are parallelograms
and whose bases are a pair of identical parallel polygons. A
polygon is a simple closed figure whose sides are line segments.
Bases
Rectangular prism Pentagonal prism Triangular prism
The volume of a solid is the number of cubes it takes to fill the solid.
The volume of a prism is found by multiplying the area of the base (B)
by the height of the prism. The height is the distance between the
2 bases.
BhV
Find the volume of a rectangular prism that has length of 7cm, with
of 6 cm and height of 4 cm.
7 cm
6 cm4 cm
Steel weighs 0.28 . What is the weight of a rectangular piece of steel 0.25 in. by 15.0 in. by 32.0 in?
3/lb in
A cylinder is a geometric solid with a curved lateral surface. A can is
an example of a cylinder.The volume of a cylinder is given
by
hr
BhV2
r
h
Example: Find the volume of the cylinder.
3
2
4.18086
)40()12(14.3
mV
V
d = 24 m
40 m
Since d = 24, then r = 12 m.
hrV 2
The volume of any cone or pyramid is given by the formula
BhV3
1
height
Base
Slant height
diameter
height
Base
where B = area of the base
Apex
Find the volume.
3995.193
)5.6)(7.87.8(3
13
1
in
BhV
Find the volume.
3
2
2954
)6.19)(1214.3(3
13
1
in
BhV
19.6 cm
The volume of a sphere is given by the formula
3
4 3rVsphere
3
3
6.2143
3
814.34
m
V
The lateral surface area is the sum of the areas of the lateral faces of
the prism.LSA = ph,
where p is the perimeter of the base and h is the height of the
prism.
Find the lateral surface area of a rectangular prism that has length of
7cm, with of 6 cm and height of 4 cm.
7 cm
6 cm4 cm
Front and back = 4 x 7 each = 2(28) = 56 sq. cm.
2 ends = 4 x 6 each = 2(24) = 48 sq. cm.
Lateral surface area = 104 sq. cm.
The total surface area is found by finding the sum of the lateral area faces and the areas of the bases.
TSA = ph + 2B
7 cm
6 cm4 cm
Lateral surface area = 104 sq. cm.
The top and bottom are the bases.Top area = 6 x 7 = 42 sq. cm.Same for the bottom = 42 sq. cmArea of the bases = 2(42) = 84 sq. cm.
Total S.A. = 104 + 84 = 188 sq. cm.
The lateral surface area of a cylinder and be visualized by taking a can,
cutting out the top and bottom, then down the side and unrolling the can. The resulting shape is a rectangle
that has length equal to the circumference of the circular top and width equal to the height of the can.
The formula is
rhphASL 2...
The total surface area is the sum of the lateral area and the 2 bases
(top and bottom)
Find the lateral surface area and total surface area of the cylinder.
• Lat. S.A.=
• Total S.A.= Lat.S.A. + 2 bases, where the bases are circles
rh2
2.5 in
12 in
24.188
)12)(5.2)(14.3(2
in
rh2
2
2
65.227
25.394.188
)5.2)(14.3(24.188
in
A steel cylindrical tank needs to hold 7000 gal. Due to space constraints, the
tank should be 10 ft in diameter. How tall should the tank be? (Water weighs 8.34
lb/gal and 62.4 lb/cu.ft.) • First convert gal to cu.ft.
• Take this volume and radius of 5 ft, substitute them into the volume formula and solve for h.
..58.9354.62
..34.87000 ftcu
lb
ftcu
gal
lbgal
Example continued:
h
hrV2
2
)5(14.358.935
hft
h
92.11
5.7858.935
Find the amount of paper used for labels for 1000 cans like those
shown below.
8.24 cm
3.16 cm
Sweetheart
Chicken Soup
The total surface area of a sphere is given by TSA = 4πr²
2
2
2
84.803
814.34
4
m
rTSA
Lateral surface area of a cone is given by
LSA = πrs, where r is the radius and s is the slant height,
and the total surface area is given by
TSA = πrs + πr²
Find the lateral surface area and total surface area of a cone that
has a radius of 6 ft, slant height of 10 ft and height of 8 ft.
24.188
10614.3
ft
rsLSA
2
2
2
44.301
04.1134.188
614.34.188
ft
rrsTSA
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