# A solid cube is cut into 2 cuboids with equal volumes.Find the ratio of the total surface area of one of the cuboids to that of the cube

2
by nneehhaa66

## Answers

• Brainly User
2015-02-08T18:44:25+05:30
The surface area of a cub is 6*(area of one face) = 6LW
The volume of a cube is LWH
acube = 6LW

to make two equal cuboids, we cut the cube in half through its height - LW(.5H)
The surface area of the cuboid is
base + top + four sides
LW + LW + 4(.5HL)
2LW + 2LH
acuboid = 2L(W+H)

so the ratio of the cube to the cuboid is
acube : acuboid
6LW : 2L(W+H)
now, the important part, since we started with a cube L = W = H, so we can simplify
6LL : 2L(L+L)
6L^2 : 2L(2L)
6L^2 : 4 L^2
6:4
3:2
2015-02-08T19:15:34+05:30

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Let the side of solid cube = a
TSA of cube = 6a²

When the cube is cut into two cuboid with equal volume, the cube will be cut into two equal halves through its side.
the cuboid thus formed will have dimension,
length (l)= a
breadth (b)= a
height (h)= a/2
TSA = 2 (lb + bh + lh)
= 2 (a² + a²/2 + a²/2)
= 2 (2a²)
= 4a²

Ratio = (TSA of cuboid) : (TSA of cube) = 4a² : 6a² = 2:3
The Ratio is 2:3.