VOLUME OF TRIANGULAR PRISMS AND CYLINDERS

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.

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

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.

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

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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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

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

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

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

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

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

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

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

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