Surface Area and Volume

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By Pythagoras theorem in the right triangle formed: l² = h² + r² This means: (slant height)² = (perpendicular height)² + (base radius)²

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Curved surface area of a cone = πrl Where: r = radius of the base l = slant height of the cone This formula comes from the area of the sector when the cone is unfolded.

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Total surface area of a cone = πr(l + r) This equals: Curved surface area + Base area = πrl + πr² = πr(l + r) Where r is radius and l is slant height.

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Volume of a cone = (1/3) × πr²h Where: r = radius of the base h = perpendicular height This is one-third the volume of a cylinder with the same base and height.

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When a cone is unfolded, its curved surface forms a sector of a circle. • The radius of the sector = slant height (l) of the cone • The arc length of the sector = circumference of the base (2πr) • Th

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Volume of cone = (1/3) × Volume of cylinder Or: 3 × Volume of cone = Volume of cylinder This means you need 3 cones full of material to fill 1 cylinder of the same base radius and height.

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Surface area of a sphere = 4πr² Where r is the radius of the sphere. This can be remembered as 4 times the area of a circle with the same radius.

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Volume of a sphere = (4/3)πr³ Where r is the radius of the sphere. This is four-thirds times π times the cube of the radius.