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