Answer :

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} + h^{2}

l = √ (6-2)^{2} + 8^{2}

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

Total surface area of frustum =

= =

= 350.591cm^{2}

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