Question

② the ratio between the lengths of the
edges of 2 cubes are in the ratio 3:2
find the ratio between there .
☺'s total durdace area
(1) Volume​

Answer 1

Answer:

=8×3/8×2

=24/16

=24:16

is the ratio

Answer 2

Answer:

$\bigstar{\bold{Ratio\:between\:their\:TSA=9:4}}$

$\bigstar{\bold{Ratio\:between\:their\:volumes=27:8}}$

Step-by-step explanation:

$\Large{\underline{\bf{Given:}}}$

• Ratio between the lengths of edges of 2 cubes are in the ratio 3 : 2

$\Large{\underline{\bf{To\:Find:}}}$

• Ratio between their total surface area
• Ratio between their volumes

$\Large{\underline{\bf{Solution:}}}$

➝ Here we have to find the ratio between the surface areas and volumes of the cubes.

➝ Let us assume the edge of the first cube as 3x units

➝ Let the edge of the second cube be 2x units

➝ The total surface area of a cube is given by,

    TSA of a cube = 6a²

    where a is a side/edge of the cube

➝ Hence,

    TSA of first cube = 6 × (3x)²

    TSA of first cube = 6 × 9x²

   TSA of first cube = 54 x² unit²

➝ Also,

    TSA of second cube = 6 × (2x)² units

     TSA of second cube = 6 × 4x²

     TSA of second cube = 24 x²unit²

➝ Therefore ratio of their total surface areas is given by,

    $\sf \dfrac{TSA\:of\:first\:cube}{TSA\:of\:second\:cube} =\dfrac{54x^{2} }{24x^{2} }$

   

     $\sf \dfrac{TSA\:of\:first\:cube}{TSA\:of\:second\:cube} =\dfrac{9 }{4 }$

➝  Hence ratio of their total surface area is 9 : 4.

     $\boxed{\bold{Ratio\:between\:their\:TSA=9:4}}$

➝  Now finding the ratio of their volumes,

➝  Volume of a cube is given by,

     Volume of a cube = a³

     where a is a side of the cube

➝ Therefore,

    Volume of the first cube = (3x)³

    Volume of the first cube = 27x³unit³

➝  Also,

     Volume of the second cube = (2x)³

     Volume of the second cube =  8x³unit³

➝  Now ratio of their volumes is given by,

     $\sf \dfrac{Volume\:of\:first\:cube}{Volume\:of\:second\:cube} =\dfrac{27x^{3} }{8x^{3} }$

   $\sf \dfrac{Volume\:of\:first\:cube}{Volume\:of\:second\:cube} =\dfrac{27 }{8 }$

➝ Hence ratio of their volumes is 27 : 8.

    $\boxed{\bold{Ratio\:between\:their\:volumes=27:8}}$