two cubes have their volumes in the ratio 8:125 what is the ratio of their surface areas - Maths - Surface Areas and Volumes

Question

two cubes have their volumes in the ratio 8:125 what is the
ratio of their surface areas?

Vimala · Accepted Answer

Volume of a cube whose side is l units is

$V = l^{3} u n i t^{3}$ .

Total surface area of a cube whose side is l units is

$A = 6 l^{2} u n i t^{2}$ ]

It is given that the ratio of the volume of two cubes is

$\frac{V_{1}}{V_{2}} = \frac{8}{125}$

Let the side of the first cube be $l_{1}$ and that of thye other be $l_{2}$ .

Thus,

$\frac{{l_{1}}^{3}}{{l_{2}}^{3}} = \frac{8}{125}$

Taking cube root on both sides,

$\frac{l_{1}}{l_{2}} = \frac{2}{5}$

Now, squaring both the sides,

$\frac{{l_{1}}^{2}}{{l_{2}}^{2}} = \frac{4}{25}$

Multiply the numerator and denominator by 6 on both the sides.

$\frac{6 {l_{1}}^{2}}{6 {l_{2}}^{2}} = \frac{24}{150}$

Thus, the ratio of the surface areas of the two cubes is

$\frac{A_{1}}{A_{2}} = \frac{24}{150}$

two cubes have their volumes in the ratio 8:125. what is the ratio of their surface areas?