Volume and Surface Area of Solid Figures
 The volume of a cube is 512 cm^{3}, Its surface area is ?

 64 cm^{2}
 256 cm^{2}
 384 cm^{2}
 512 cm^{2}

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∵ a^{3} = 512 = 8 x 8 x 8
⇒ a = 8 cm
∵ Surface area = 6a^{2}Correct Option: C
∵ a^{3} = 512 = 8 x 8 x 8
⇒ a = 8 cm
∵ Surface area = 6a^{2}
=[6 x (8)^{2}] cm^{2}
=384 cm^{2}
 The surface area of a cube is 726 m^{2}. Its volume is ?

 1300 m^{3}
 1331 m^{3}
 1452 m^{3}
 1542 m^{3}

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Surface area = 6a2 = 726
Correct Option: B
Surface area = 6a^{2} = 726
⇒ a^{2} = 121
⇒ a = 11 cm
∴ Volume of the cube = (11 x 11 x 11) cm^{3}
= 1331 cm^{3}
 If each side of a cube is doubled, then its volume? .

 Is doubled
 Becomes 4 times
 Becomes 6 times
 Becomes 8 times

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Let the edge of original cube = x cm
Edge of new cube = (2x) cm
Ratio of their volumes = x^{3} : (2x)^{3}Correct Option: D
Let the edge of original cube = x cm
Edge of new cube = (2x) cm
Ratio of their volumes = x^{3} : (2x)^{3}
= x^{3} : 8x^{3}
= 1 :8
Thus the volumes be comes 8 times.
 Three metal cubes of sides 5 cm, 4 cm and 3 cm are melted and recast into a new cube. The length of the edge of this cube, is ?

 6 cm
 8 cm
 10 cm
 None of these

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Volume of new cube = (5)^{3} + (4)^{3} + (3)^{3} cm^{3}
Correct Option: A
Volume of new cube = (5)^{3} + (4)^{3} + (3)^{3} cm^{3}
= 126 cm^{3}
Edge of this cube = (6 x 6 x 6)^{1/3} = 6 cm
 If the volumes of two cubes are in the ratio 8 : 1, the ratio of their edges, is ?

 8 : 1
 2√2 : 1
 2 : 1
 None of these

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Volume of new cube = [(5)^{3} + (4)^{3} + (3)^{3}] cm^{3}
Correct Option: A
Volume of new cube = [(5)^{3} + (4)^{3} + (3)^{3}] cm^{3}
= 216 cm^{3}
Edge of this cube = ( 6 x 6 x 6)^{1/3} = 6 cm