A largest cone is cut off from a cube with core 14 cm. The volume of c

1.	A largest cone is cut off from a cube with core 14 cm. The volume of cone is :(A) 766.18 cm3(B) 817.54 cm3(C) 1232 cm3(D)718.66 cm3
Answer» Answer is (D)718.66 cm³ A Largest cone is cut off from a cube with its core 14 cm. ∴ Height of cone = 14 cm And diameter of base = 14 cm ∴ Base radius of cone = \(\frac { 14 }{ 2 }\) = 7 cm Volume of cone = \(\frac { 1 }{ 3 }\)πr²h = \(\frac { 1 }{ 3 }\) × \(\frac { 22 }{ 7 }\) × (7)² × 14 = \(\frac { 1 }{ 3 }\) × \(\frac { 22 }{ 7 }\) × 7 × 7 × 14 = \(\frac { 1 }{ 3 }\) × 22 × 7 × 14 = \(\frac { 22\times 98 }{ 3 } \) = \(\frac { 2156 }{ 3 }\) = 718.66 cm³

A largest cone is cut off from a cube with core 14 cm. The volume of cone is :(A) 766.18 cm3(B) 817.54 cm3(C) 1232 cm3(D)718.66 cm3

Answer»

Answer is (D)718.66 cm³

A Largest cone is cut off from a cube with its core 14 cm.

∴ Height of cone = 14 cm

And diameter of base = 14 cm

∴ Base radius of cone = \(\frac { 14 }{ 2 }\) = 7 cm

Volume of cone = \(\frac { 1 }{ 3 }\)πr²h

= \(\frac { 1 }{ 3 }\) × \(\frac { 22 }{ 7 }\) × (7)² × 14

= \(\frac { 1 }{ 3 }\) × \(\frac { 22 }{ 7 }\) × 7 × 7 × 14

= \(\frac { 1 }{ 3 }\) × 22 × 7 × 14

= \(\frac { 22\times 98 }{ 3 } \)

= \(\frac { 2156 }{ 3 }\)

= 718.66 cm³