# Surface Area of a Right Circular Cone

**Surface Area of a Right Circular Cone**

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Area of the curved surface of a cone = prl = pr Â sq. units where *l*=

Total surface area of a cone = prl + pr^{2 }= pr(l + r)Â sq. units

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How many meters of cloth of 5m wide will be required to make a conical tent, the radius of the whole base is 7m and whose height is 24m ?

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Given , r=7m

Â Â Â Â Â Â Â Â h = 24m

Â Â Â Â Â Â Â Â Â l== = = 25

CSA of the cone = rl m^{2} = 7 25 = 550m^{2}

Area of the canvas used = 550m^{2}

Given , width of the canvas = 5m

Length of the canvas used = = m

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From a cylinder of 12 m height and base radius 5 m, a conical cavity of the same height and same radius (base) is carved out. Find the whole surface area of the remaining solid.

Surface area of the remaining solid= Area of a circle (base) + Area of the curved surface of the cylinder + Area of the curved surface of the cone.

= pr^{2 }+ 2prh + prl

Â l = = = 13 m

\Total curved surface area = p(r^{2 }+ 2rh + rl)

Â Â Â Â Â Â Â Â Â Â Â Â Â = Â´ (5^{2} + 2 Â´ 5 Â´ 12 + 5 Â´ 13)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â = Â´ 5(5 + 24 + 13)

Â Â Â Â Â Â Â Â Â Â Â Â Â = 660 m^{2 }

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SurfaceÂ areaÂ ofÂ theÂ remainingÂ solidÂ = 660 m^{2 }

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