Q17 of 47 Page 1

In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid.


We have to find the surface area of the frustum BCQP.


Given: AR = 4cm


AD = 12cm


∠ ARQ = ∠ADC = 90°


∠ A = ∠ A (common)


ΔAQR∼ ΔACD (by AA)


⇒


⇒ QR = 2cm


Radius of the bigger cone = R = 6cm


Radius of the smaller cone = r = 2cm


Height of the frustum = RD = 12-4 = 8cm


Slant height of the frustum:


l = √(R-r)2 + h2


l = √ (6-2)2 + 82


l = √ 16 + 64 = √80 = 4√5 = 4 × 2.236 = 8.944cm


Total surface area of frustum =


= =


= 350.591cm2


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