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

To find the volume of the larger solid, we can use the area ratio and the volume of the smaller solid. We set up a proportion and solve for the volume of the larger solid.

Step-by-step explanation:

To find the volume of the larger solid, we can use the area ratio and the volume of the smaller solid. The area ratio is given as 169:289 and the volume of the smaller solid is 689,858 cm³. We can set up a proportion:

169/289 = 689,858/V

Cross multiplying, we get:

169V = 289 * 689,858

Dividing both sides by 169, we find:

V = (289 * 689,858) / 169

Simplifying the expression, we get:

V = 1,477,326 cm³

Answer 2

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 (x^2)/(y^2)=(169)/(289)\\\\\Rightarrow (x)/(y)=(13)/(17)`

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

`\Rightarrow \left((13)/(17)\right)^3=(689,858)/(V)\\\\\Rightarrow V=689,858* (17^3)/(13^3)\\\\\Rightarrow V=314* 17^3\\\\\Rightarrow V=1,542,682\ cm^3`

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