Question

two cubes have their volumes in the ratio 1 ratio 27 find the ratio of their surface areas

Answer 1

Hey dear

Your answer is here


➡️➡️Here given two cube

➡️ Ratio of volume of two cube are = 1:27



Formula of volume of cube= ( length) ³


Suppose volume of first cube is V1 & volume Of second Cube is V2


$\frac{v1}{v2} = \frac{1}{27} \\ \\ \\ \frac{ {l1}^{3} }{ {l2}^{3} } = \frac{1}{27} \\ \\ \\ \frac{l1}{l2} = \frac{1}{3} \\ \\ \\ we \: will \: find \: to \: ratio \: of \: surface \: area \: of \: cube \\ \\ \\ formula \: of \: surface \: area \: of \: cube \: = 6 {l}^{2} \\ \\ \\ ratio \: of \: surface \: area \: of \: cube \: = \frac{6 {l1}^{2} }{6 {l2}^{2} } \\ \\ \\ = \frac{ {l1}^{2} }{ {l2}^{2} } = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9} \\ \\ \\ \\ \frac{1}{9} \: is \: your \: answer \\ \\ \\ hope \: it \: helpful \\ \\ - - - - -$

Answer 2

Here your answer✍️

Volume of Two cubes=1:27
Volume of cube=(edge)³

Edge of first Cube
a³=1
a=³√1
a=1

Edge of second cube
a³=27
a=³√27
a=3

Now edge Ratio=1:3

Surface Area=6a²

Surface Area of first Cube
=6×1²

Surface Area of second cube
=6×3²

$Ratio = \frac{6 \times {1}^{2} }{6 \times 3 {}^{2} } \\ Ratio = \frac{1 {}^{2} }{3 {}^{2} } \\ = \frac{1}{9}$
Ratio of surface area=1:9