# 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

Log in to add a comment

by nneehhaa66

Log in to add a comment

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

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

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**.

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