Question

A cube has a edge of 8 cm it is cur into two equal parts calculate the ratio of total surface area

Answer 1

`Ratio = 3: 2`

Explanation:

Given

Shape: Cube

`L = 8cm`

The surface area is calculated as:

`Area = 6*L^2`

`A_1 = 6*8^2`

`A_1 = 384`

When it is cut by half; the length is affected; so, it forms a cuboid of the following dimension:

`L = (8)/(2) = 4` --- Length

`W = 8cm` --- Width

`H = 8cm` --- Height

The surface area is:

`Area = 2 *(L*W + H * L + W * H)`

`A_2 = 2 *(4*8 + 8 *4 + 8 * 8)`

`A_2 = 2 *128`

`A_2 = 256`

So, the ratio of surface area is:

`Ratio = A_1 : A_2`

`Ratio = 384 : 256`

Divide by 128

`Ratio = 384/128 : 256/128`

`Ratio = 3: 2`