Question

A solid cone is cut into 2 cuboid of equal volume.find the ratio between the surface area of the cube and the surface area of cone of the cuboid .

Answer 1

The surface area of a cube 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

Hope it helps