Question

The area ratio of two similar soilds is 169:289 if the volume of the smaller solid is 689,858 cm what is the volume of the larger solid

Answer 1

Answer: $1,542,682\ cm^3$

Step-by-step explanation:

Given

The ratio of two similar figures is 169:289

Suppose, their length ratio is x:y

$\therefore \dfrac{x^2}{y^2}=\dfrac{169}{289}\\\\\Rightarrow \dfrac{x}{y}=\dfrac{13}{17}$

Similarly, cube of the ratio is equal to the volume ratio

$\Rightarrow \left(\dfrac{13}{17}\right)^3=\dfrac{689,858}{V}\\\\\Rightarrow V=689,858\times \dfrac{17^3}{13^3}\\\\\Rightarrow V=314\times 17^3\\\\\Rightarrow V=1,542,682\ cm^3$

Thus, the volume of the larger solid is $1,542,682\ cm^3$