PRISMS AND CYLINDERS: VOLUMES, SURFACE AREAS, AND WEIGHTS

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UNIT 28

• PRISMS AND CYLINDERS VOLUMES, SURFACE AREAS, AND
  WEIGHTS

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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

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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

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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

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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

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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
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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

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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
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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.

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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.

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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