Question

When 3 equal cubes are joined end to end surface area of resulting cuboid is 504 cm square find the edge of each cube ?

Answer 1

Answer:

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid is 648 cm

2

; find the length of edge of each cube. Also, find the ratio between the surface area of resulting cuboid and the surface area of a cube.

Given, four identical cubes are joined end to end to form a cuboid. Let the side of cube be a, then length of cuboid thus formed be 4a ,breadth be a, height be a. Surface area of resulting cuboid be 648cm

2

.

Total surface area of resulting cuboid=2(lb+bh+lh)

or,648=2(4a×a+a×a+4a×a)

or,648=2(9a

2

)

or,648=18a

2

or,a

2

=36

or,a=6cm

Length of edge of cube=6cm

Surface area of cube=6a

2

=6×6

2

=216cm

2

Ratio of surface area of resulting cuboid to cube=

216cm

2

648cm

2

=3:1

Step-by-step explanation:

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Answer 2

Answer:

Given, four identical cubes are joined end to end to form a cuboid. Let the side of cube be a, then length of cuboid thus formed be 4a ,breadth be a, height be a. Surface area of resulting cuboid be 648cm

2

.

Total surface area of resulting cuboid=2(lb+bh+lh)

or,648=2(4a×a+a×a+4a×a)

or,648=2(9a

2

)

or,648=18a

2

or,a

2

=36

or,a=6cm

Length of edge of cube=6cm

Surface area of cube=6a

2

=6×6

2

=216cm

2

Ratio of surface area of resulting cuboid to cube=

216cm

2

648cm

2

=3:1