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Question

Question 6
Derive the formula for the curved surface area and total surface area of the frustum of cone.

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Solution

Let ABC be a cone. A frustum DECB is cut by a plane parallel to its base. Let r1 and r2 be the radii of the end of the frustum of the cone and h be the height of the frustum of the cone.
In ΔABG and Δ ADF,DF||BG
ΔABGΔADF
DFBG=AFAG=ADAB
f2r1=h1hh1=l1ll1
r2r1=1hh1=1ll1
1hh1=r2r1
hh1=1r2r1=r1r2r1
h1h=r1r1r2
h1=r1hr1r2
Volume of frustum of cone = Volume of cone ABC - Volume of cone ADE

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