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Published byLester Houston Modified over 9 years ago

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VOLUME OF TRIANGULAR PRISMS AND CYLINDERS

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MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. Objective: Understand how to calculate the volume of triangular prisms and cylinders. Learning target: Answer at least 3 of the 4 volume questions correctly on the exit ticket.

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What do prisms and cylinders have in common? They are both 3-dimensional shapes with two identical ends.

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How do we find the volume of a prism or cylinder? Calculate the area of one end using that shape’s area formula. Take that area and multiply it by the height to get the volume.

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What is the volume of this triangular prism? Find the area of one of the triangle ends: Area of triangle = ½ × base × height = ½ × 6 cm × 4 cm = 3 cm × 4 cm = 12 cm² Multiply this area by the “height” (height of the prism, not height of the triangle) Volume = 12 cm² × 9 cm = 108 cm³

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What is the volume of this triangular prism? Find the area of one of the triangle ends: Area of triangle = ½ × base × height = ½ × 3 in × 4 in = ½ × 12 in² = 6 in² Multiply this area by the “height” Volume = 6 in² × 2 in = 12 in³

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Answering using iPads Open up Safari in your iPad Go to www.m.socrative.comwww.m.socrative.com For the Room Number, type in: MrPMath Click “Join Room” Wait for more instructions!

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What is the volume of this triangular prism? Find the area of one of the triangle ends: Area of triangle = ½ × base × height = ½ × 8 cm × 9 cm = 4 cm × 9 cm = 36 cm² Multiply this area by the “height” Volume = 36 cm² × 5 cm = 180 cm³

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What is the volume of this triangular prism? Find the area of one of the triangle ends: Area of triangle = ½ × base × height = ½ × 8 cm × 4 cm = 4 cm × 4 cm = 16 in² Multiply this area by the “height” Volume = 16 in² × 12 in = 192 in³

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What is the volume of this cylinder? Find the area of one of the circle ends: Area of circle = π × radius² = π × (7 cm)² = π × 7 cm × 7 cm = 49π cm² Multiply this area by the height Volume = 49π cm² × 12 cm = 588 π cm³

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What is the volume of this cylinder? Find the area of one of the circle ends: Area of circle = π × radius² = π × (5 cm)² = π × 5 cm × 5 cm = 25π cm² Multiply this area by the height Volume = 25π cm² × 10 cm = 250π cm³

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What is the volume of this cylinder? Find the area of one of the circle ends: Area of circle = π × radius² = π × (4 cm)² = π × 4 cm × 4 cm = 16π cm² Multiply this area by the height Volume = 16π cm² × 12 cm = 192π cm³

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What is the volume of this cylinder? Find the area of one of the circle ends: Radius = 10 cm ÷ 2 = 5 cm Area of circle = π × radius² = π × (5 cm)² = π × 5 cm × 5 cm = 25π cm² Multiply this area by the height Volume = 25π cm² × 12 cm = 300π cm³

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Direct Station We will use the whiteboards to practice volume problems.

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Collaborative Station: Create Your Own Shape Each problem will give you a required volume. You must correctly choose a base/height/radius of your shape in order to get that volume. Example: Create a triangular prism with a volume of 12 in³. Sample answers: or

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Independent Station Continue ST Math’s unit on area and perimeter

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