Surface Area

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Surface Area Volume
Lesson 17

• Volume of Prisms

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Warm-Up

• Find the area of each figure.
• What do you know about volume? List at least 3
  things.

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Volume of Prisms

• Target Calculate the volume of prisms.

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Vocabulary

• Volume The number of cubic units needed to fill
  a solid.

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Prism Volume

• The volume of a prism is equal to the product of
• the area of the base (B) and the height (h).
• Volume (area of the base)(height)
• V Bh

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Example 1a

• Find the volume of the prism.
• V Bh
• V (6 4)(12)
• V (24)(12)
• V 288
• Volume 288 cm³

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Example 1b

• Find the volume of the prism. The base area is
  41 cm2.
• V Bh
• V (41)(10)
• V 410
• Volume 410 cm³

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Example 1c

• Find the volume of the prism.
• V Bh
• V ( 8 3)(5.7)
• V (12)(5.7)
• V 68.4
• Volume 68.4 m³

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Example 2

• Mischa can buy her favorite laundry detergent in
  two different
• shaped containers. One container is a triangular
  prism with a
• base area of 15 square inches and a height of 6
  inches. She can
• also buy the detergent in a rectangular prism
  container with a
• length of 5 inches, a width of 4 inches and a
  height of 4.5
• inches. Which container has the most volume?
• Triangular box

Rectangular box
V Bh V (15)(6) 90
V Bh V (5 4)(4.5) (20)(4.5) 90
Both boxes are the same size 90 cubic inches!
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Exit Problems

• Find the volume of the prism.
• A cereal box is a rectangular prism. It is 10
  inches long, 14 inches tall and 3 inches wide.
  Find the volume of the cereal box.

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Communication Prompt

• What type of prism is easiest for you to find the
  volume of? What type of prism is most difficult
  for you to find the volume of? Explain.
• Explain how the formula on the Oregon State
  Assessment Formula sheet (lwh) and Bh are the
  same.