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Published byAdele Matthews Modified over 5 years ago
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What is the relationship between the volume of a cylinder and the volume of a cone? Watch the following video to find out!
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Since it takes three cones to fill one cylinder,
i.e. 3 Vcone = Vcylinder then to isolate a formula for volume of a cone: 3 Vcone = Vcylinder Vcone = Vcylinder 3
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What is the relationship between the volume of a cube and the volume of a square-based pyramid? Watch the following video to find out!
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Since it takes three pyramids to fill one cube,
Ad Since it takes three pyramids to fill one cube, i.e. 3 Vpyramid = Vcube then to isolate a formula for volume of a pyramid: 3 Vpyramid = Vcube Vpyramid = Vcube 3
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In general, the volume of a cone or pyramid:
where A is the area of the base and h is the height from apex to base. V = Ah 1 3 s a A square = Iength2 A circle = r2
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Part C – Volume of Pyramids and Cones PYTHAGOREAN ALERT!
[NB: slant height (s) height of the pyramid (h)] a Example: A square-based pyramid has a slant height of 15 cm and apothem of 12 cm. Find the volume. Equation: Substitute: Solve: To find Asquare-base: A = (length)2 A = (2a)2 A = 4a2 A = 4(12)2 A = 576 To find height: h2 + a2 = s2 h = 152 h2 = h2 = 225 – 144 h2 = 81 h = 9 (sqrt both sides) V = 1/3 Ah V = 1/3 (576) (9) V = 1728 h s=15 a a=12 a+a=2a The volume of the pyramid is 1728 cm3
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