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UNIT 28

- PRISMS AND CYLINDERS VOLUMES, SURFACE AREAS, AND

WEIGHTS

PRISMS

- A polyhedron is a three-dimensional (solid)

figure whose surfaces are polygons - A prism is a polyhedron that has two identical

(congruent) parallel polygon faces called bases

and parallel lateral edges - Prisms are named according to the shape of their

bases, such as triangular, rectangular,

pentagonal, and octagonal - The volume of any prism is equal to the product

of the base area and the altitude

VOLUME OF A PRISM

- Compute the volume of the prism shown below

- V ABh

- This prism has a rectangular base so
- AB length ? width

AB (60cm)(20cm) 1200 cm2

- Now, V ABh
- (1200 cm2)(25 cm)
- 30000 cm3 Ans

CYLINDERS

- A circular cylinder is a solid that has identical

circular parallel bases - The surface between the bases is called the

lateral surface. - The altitude (height) of a circular cylinder, is

a perpendicular segment that joins the planes of

the bases - The axis of a circular cylinder is a line that

connects the centers of the bases - In a right circular cylinder the axis is

perpendicular to the bases - The volume of right circular cylinders is the

same as prisms - V ABh

VOLUME OF A CYLINDER

- Find the volume of the cylinder shown below given

that the bases have a radius of 16 centimeters

- V ABh

- The cylinder has a circular base, so
- AB ?r2 ?(16 cm)2 804.248 cm2

50 cm

- Now, V ABh
- (804.248 cm2)(50 cm)
- 40212.39 cm3 Ans

TRANSPOSING VOLUME FORMULAS

- An engine piston has a height of 18.6 centimeters

and a volume of 460 cubic centimeters. Find the

radius of the piston

- The piston is a circular cylinder, so V ABh

?r2h

- Substitute the given measurements into the

formula and solve for r

V ?r2h 460 cm3 ?r2(18.6 cm)

r 2.806 cm Ans

LATERAL AND SURFACE AREAS

- The lateral area of a prism is the sum of the

areas of the lateral faces. The lateral area of a

cylinder is the area of the curved or lateral

surface - The lateral area of a right prism equals the

product of the perimeter of the base and height - The lateral area of a right circular cylinder is

equal to the product of the circumference of the

base and height - The surface area of a prism or a cylinder equals

the sum of the lateral area and the two base areas

SURFACE AREA EXAMPLE

- Find the surface area of the circular cylinder

below given that it has a radius of 8 inches

- The surface area is equal to the sum of the
- lateral area and the two base areas

- Lateral area CBh

2?(8)(40)

2010.62 in2

- Area of base ?r2

?(8)2 201.062 in2

- Surface area 2010.62 201.062 201.062

2412.744 in2 Ans

PRACTICE PROBLEMS

- 1. Find the volume of a rectangular prism with a

length of 10 meters, width of 15 meters, and

height of 20 meters. - 2. Determine the lateral area of the prism in

problem 1. - 3. Compute the surface area of the prism is

problem 1. - 4. Find the volume of a triangular prism given

that the triangular bases have sides of 8 inches,

10 inches, and 12 inches and that the prism has a

height of 5 inches. - 5. Compute the volume of a right circular

cylinder with a radius of 15 mm and a height of

25 mm.

PRACTICE PROBLEMS

- 6. Find the lateral area of the cylinder in

problem 5. - 7. Find the surface area of the cylinder in

problem 5. - 8. Find the diameter of a right circular

cylinder given that it has a volume of 150 cubic

feet and a height of 12.5 feet. - 9. A solid steel post 27.6 inches long has a

square base. The post has a volume of 110 cubic

inches. Compute the length of a side of the base. - 10. Find the lateral area of a box with a length

of 18 inches, width of 14 inches, and height of

12 inches.

PROBLEM ANSWER KEY

- 1. 3000 m3
- 2. 1000 m2
- 3. 1300 m2
- 4. 198.431 in3
- 5. 17671.46 mm3
- 6. 2356.19 mm2
- 7. 3769.91 mm2
- 8. 3.91 feet
- 9. 1.996 inches
- 10. 768 in2

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