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?

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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?

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Answer 1 · 2018-02-16T14:15:15

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

As the cylinders are similar we can say $\frac{R}{r} = \frac{H}{h}$ $R/r=H/h$

Now volume of smaller cylinder is $π r^{2} h = 125$ $pir^2h=125$ and that of larger one is $π R^{2} H = 343$ $piR^2H=343$

So $\frac{π R^{2} H}{π r^{2} h} = \frac{343}{125}$ $(piR^2H)/(pir^2h)=343/125$

$\Rightarrow \frac{H^{2}}{h^{2}} \times \frac{H}{h} = \frac{343}{125}$ $=>H^2/h^2xxH/h=343/125$

$\Rightarrow \frac{H^{3}}{h^{3}} = \frac{7^{3}}{5^{3}}$ $=>H^3/h^3=7^3/5^3$

$\Rightarrow \frac{H}{h} = \frac{7}{5}$ $=>H/h=7/5$

$\Rightarrow H = \frac{7}{5} \times h = \frac{7}{5} \times 5 = 7$ $=>H=7/5xxh=7/5xx5=7$ ft

Answer 2 · 2018-02-16T14:19:16

$7 feet$ $7" feet"$

Explanation:

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

$∙ linear ratio = a : b$ $• " linear ratio "=a:b$

$∙ area ratio = a^{2} : b^{2}$ $• " area ratio "=a^2:b^2$

$∙ volume ratio = a^{3} : b^{3}$ $• " volume ratio "=a^3:b^3$

$here volume ratio = 343 : 125$ $"here volume ratio "=343:125$

$\Rightarrow linear ratio = \sqrt[3]{343} : \sqrt[3]{125} = 7 : 5$ $rArr"linear ratio "=root(3)(343):root(3)(125)=7:5$

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

$\Rightarrow height of the larger cylinder = 7 feet$ $rArr"height of the larger cylinder "=7" feet"$

Answer 3 · 2018-03-20T21:28:02

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

Explanation:

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

$\times \times \times \times x {heights}^{3} volumes$ $color(white)(xxxxxxxxx)"heights"^3" volumes"$

$\frac{smaller \to}{larger \to} = \frac{5^{3}}{x^{3}} = \frac{125}{343}$ $("smaller" rarr)/("larger"rarr) = 5^3/x^3 " "= 125/343$

$x^{3} = \frac{5^{3} \times 343}{125}$ $x^3 = (5^3 xx 343)/125$

$x^{3} = 343$ $x^3 = 343$

$x = 7$ $x =7$

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

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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?

3 Answers

Explanation:

Explanation:

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Science

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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?

3 Answers

Explanation:

Explanation:

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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?