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The radius and height of a right solid circular cone (ABC) are respectively 6 cm and 2√7 cm. A coaxial cone (DEF) of radius 3 cm and height √7 cm is cut out of the cone as shown in the given figure. What is the whole surface area of the solid thus formed ? 

(a) 96 π cm2 

(b) 87 π cm2 

(c) 60 π cm2

(d) 36 π cm2

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Best answer

(b) 87 π cm2

Radius and height of cone ABC are 6 cm and 2√7 cm respectively.

∴ Slant height of cone ABC = \(\sqrt{6^2+(2\sqrt7)^2}\)

\(\sqrt{36+28}=\sqrt{64} = 8\) cm

∴ Curved surface area of cone ABC = π x 6 x 8 = 48π cm2 

Also radius and height of cone DEF are 3 cm and √7 respectively 

∴ Slant height of cone DEF = \(\sqrt{3^2+(\sqrt7)^2}\)

= \(\sqrt{9+7}=\sqrt{16} = 4\) cm.

∴ Curved surface area of cone DEF = π x 3 x 4 = 12π cm2 

∴ Whole surface area of remaining solid 

= Curved surface area of cone ABC + Area of base + Curved surface area of cone DEF 

= 48 π + π(62 – 32) + 12π 

= 48π + π(36 – 9) + 12π = 87 π cm2.

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