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

Answer:

$Ratio = 3: 2$

Step-by-step 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:

$L = \frac{8}{2} = 4$ --- 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

$Ratio = 384/128 : 256/128$

$Ratio = 3: 2$