Question

Each edge of a cube is decreased by 50%..find the ratio of the volume of original nd reduced cube

Answer 1

$let \: \: edge \: \: of \: \: cube \: \: be \: \: x \\ after \: \: decrease \: \: edge \: \: is \: \: 0.5x \\ ratio = \frac{ {x}^{3} }{ {(0.5x)}^{3} } = 8$

Answer 2

The ratio of the volume of original cube and reduced cube is 8:1

Given

• Each edge of a cube is decreased by 50%

Explanation:

FORMULA

$\circ {\boxed{\underline{\sf{ Volume_{(Cube)} = a^3 }}}}$

Let the original edge of the cube be x

again,

Edge of cube After reduction = x/2

Equations be like:-

${\sf{ Earlier \ Volume = x^3 \cdots \cdots (1) }}$

${\sf{ After \ Reduction \ Volume = \left( \dfrac{x}{2} \right)^3 \cdots \cdots (2) }}$

Now, We can compare both Volumes as:-

$\colon\implies{\sf{ \dfrac{x^3}{ \left( \dfrac{x}{2} \right)^3 } }} \\ \\ \\ \colon\implies{\sf{ \dfrac{x^3}{ \left( \dfrac{x^3}{8} \right) } }} \\ \\ \\ \colon\implies{\sf{ \dfrac{ \cancel{x^3} \times 8}{ \cancel{x^3} } }} \\ \\ \\ \colon\implies{\sf{ \dfrac{8}{1} }} \\ \\ \\ \colon\implies{\boxed{\mathfrak\pink{8 \colon 1 }}}$

Hence,

• The ratio of the volume of original cube and reduced cube is ${\sf\bold\green{ 8 \colon 1 }}$.