Question

Two cylinders are similar. The volume of the larger cylinder is 343 ft³ and the volume of the smaller cylinder is 125 ​​ft³. The height of the smaller cylinder is 5 ft. What is the height of the larger cylinder?

Answer 1

Let the radius of smaller cylinder be `r`ft and its height be `h`ft.Again the radius of larger cylinder is `R` ft and its height is `H` ft. Given `h=5` ft

As the cylinders are similar we can say `R/r=H/h`

Now volume of smaller cylinder is `pir^2h=125` and that of larger one is `piR^2H=343`

So `(piR^2H)/(pir^2h)=343/125`

`=>H^2/h^2xxH/h=343/125`

`=>H^3/h^3=7^3/5^3`

`=>H/h=7/5`

`=>H=7/5xxh=7/5xx5=7` ft

Answer 2

`7" feet"`

Explanation:

`"given "color(blue)"similar figures ""then"`

`• " linear ratio "=a:b`

`• " area ratio "=a^2:b^2`

`• " volume ratio "=a^3:b^3`

`"here volume ratio "=343:125`

`rArr"linear ratio "=root(3)(343):root(3)(125)=7:5`

`"5 is the height of the smaller cylinder"`

`rArr"height of the larger cylinder "=7" feet"`

Answer 3

The height of of the larger cylinder is `7` ft

Explanation:

The volumes of similar figures are in the same ratio as the cube of their heights,

`color(white)(xxxxxxxxx)"heights"^3" volumes"`

`("smaller" rarr)/("larger"rarr) = 5^3/x^3 " "= 125/343`

`x^3 = (5^3 xx 343)/125`

`x^3 = 343`

`x =7`

The height of of the larger cylinder is `7` ft