The Cone (Leaving Cert Mathematics): Flashcards

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The Cone
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Cone definition

3D shape with circular base tapering to a single point (vertex)

Right circular cone

Cone with vertex directly above centre of circular base

Perpendicular height (h) in a cone

Vertical distance from vertex to centre of base

Slant height (l) of a cone

Distance from vertex to any point on edge of base

Radius (r) of a cone

Distance from centre of base to its edge

Pythagoras relation for cone measurements

l2=h2+r2l^2 = h^2 + r^2

Volume formula for a cone

V=13πr2hV = \frac{1}{3}\pi r^2 h

Which height in cone volume formula?

Perpendicular height (h)

Curved surface area formula for cone

πrl\pi r l

Which height in curved surface area?

Slant height (l)

Total surface area of solid cone

πrl+πr2\pi r l + \pi r^2

Common cone formula mistake

Confusing perpendicular height (h) and slant height (l)

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