Question

The edges of two cubes are 8 cm and 4 cm respectively. Calculate the ratio of
their surface area ?​

Answer 1

Given :-

Edge of the first cube = 8 cm

Edge of the second cube = 4 cm

To Find :-

The surface area.  

The ratio of the surface area.

Analysis :-

Find the surface area of the 1st and 2nd cube.  

Make a ratio of 1st to the 2nd surface area of the cube and simplify it.  

Solution :-

We know that,  

$\bold{Surface\;area\;of\;a\;cube=6a^{2} }$

Given that,

Edge of the first cube = 8 cm

Substituting their values,

Surface area = $6$ × $8^{2}$

                      = $6$ × $64$

                      = $384cm^{3}$

Hence, the surface area of the 1st cube is 384 cm³

Finding for the 2nd one,

Surface area of a cube = 6a²

Given that,

Edge of the 2nd cube = 4 cm

Substituting them,

Surface area =  $6$ × $4^{2}$

                      = $6$ ×$16$

                      = $96cm^{3}$

Hence, the surface area for the 2nd cube is 96 cm³

Next, finding their ratio

                                         →384 : 96

In fractional form and simplifying,      

                                        →  $\frac{384}{96} =\frac{1}{4}$

                                        →  $1:4$

Therefore, the ratio of their surface area is 1 : 4

$\huge\red{@alurringbabe}$