The radius and height of a right solid circular cone (ABC) are respect

1.	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
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.

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

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