Question

if the surface area of two cubes are in the ratio 9: 49 , and the volume of the first cube is 216m*3 then what is the volume of the second cube?​

Answer 1

Answer:

the surface area of two cubes= 9:49

i.e.

$\frac{the \: area \: of \: 1st \: cube( {a}^{2} )}{the \: area \: of \: 2nd \: cube( {b}^{2} )} = \frac{9}{49}$

or,

$\frac{ {a}^{2} }{ {b}^{2} } = \frac{9}{49}$

or,

$\frac{ {(a)}^{2}}{( {b)}^{2}} = \frac{ {(2)}^{2} }{ {(7)}^{2} }$

or,

$\frac{a}{b} = \frac{2}{7}$

or,

$b = \frac{2a}{7} - - - (i)$

°•°

$volume \: of \: 1st \: cube = 216 {cm}^{3}$

or,

${a}^{3} = 216$

•°•

$a = 6$

From eq---(i), we get

$b = \frac{2 \times 6}{7}$

•°•

$b = \frac{12}{7}$

•°•

$the \: volume \: of \: 2nd \: cube ( {b}^{3} ) = {(\frac{12}{7} )}^{3}$

${b}^{3} = \frac{1728}{343}$

•°•

$the \: volume \: of \: 2nd \: cube = \frac{1728}{343} {cm}^{3}$

Answer 2

Answer:

The volume of the second cube is 1176 m³.

Step-by-step explanation:

• For first Cube: Suppose the length of one side of the 1st cube = a

       The total surface area of the cube = 6(length of one side)² = 6a²

       The volume of the cube = (length of one side)³ = a³

       According to given condition, Volume of this cube = a³ = 216 m³

                                                                                               a = ∛216 m

                                                                                               a = 6 m

   The surface area of this cube = 6a² = 6(6)² = 216 m²

• For second Cube: Suppose length of one side of the 2nd cube = b

       The total surface area of the cube = 6(length of one side)² = 6b²

       The volume of the cube = (length of one side)³ = b³

• Calculation of b³:

      The given ratio is:   $\frac{Surface area of 1st cube}{surface area of second cube} = \frac{9}{49}$

                                           $\frac{216}{b^3} = \frac{9}{49}$

                                           $216 \times 49 = 9b^3$

                                            $b^3 = \frac{216 \times 49}{9}$ = 24 × 49 = 1176 m³

      So, the volume of the second cube is 1176 m³.

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