Question

The lengths are in the ratio 1:2, breadths in the ratio 3 : 5, and heights in the
ratio 4: 5. Find the ratio of their volumes​

Answer 1

GIVEN :-

• Ratio of length , l = 1:2 .
• Ratio of breadth , b = 3:5 .
• Ratio of Height , h = 4:5 .

TO FIND :-

• The Ratio of volumes (v:v').

SOLUTION :-

Let ratio constant be "x".

$\\ : \implies \displaystyle \sf \: \frac{v}{v'} = \frac{l \times b \times h}{l '\times b' \times h'}$

$: \implies \displaystyle \sf \: \frac{v}{v'} = \frac{1x \times 3x \times 4x}{2x \times 5x \times 5x}$

$: \implies \displaystyle \sf \: \frac{v}{v'} = \frac{12x ^{3} }{50x ^{3} }$

$: \implies \displaystyle \sf \: \frac{v}{v'} = \frac{6}{25}$

$: \implies \underline{ \boxed{\displaystyle \sf \: \bold{ {v}:{v'} = 6:25}}}$

Hence the Ratio of volumes is 6:25.

Answer 2

Answer:

⠀⠀ ⌬ Ratio of Lengths = 1 : 2

⠀⠀ ⌬ Ratio of Breadths = 3 : 5

⠀⠀ ⌬ Ratio of Heights = 4 : 5

Let the Ratio of Volumes be A : B

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{A}{B}=\dfrac{l \times b \times h}{l' \times b' \times h'}\\\\\\:\implies\sf \dfrac{A}{B} = \dfrac{1 \times 3 \times 4}{2 \times 5 \times 5}\\\\\\:\implies\sf \dfrac{A}{B} = \dfrac{3 \times 2}{5 \times 5}\\\\\\:\implies\sf \dfrac{A}{B} = \dfrac{6}{25}\\\\\\:\implies\underline{\boxed{\sf A :B = 6 :25}}$

⠀

$\therefore\:\underline{\textsf{Required ratio of volumes is \textbf{6:25}}}.$