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# The volume of a cylindrical tank is directly proportional to the heigh

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Math Expert
Joined: 02 Sep 2009
Posts: 51281
The volume of a cylindrical tank is directly proportional to the heigh  [#permalink]

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10 Dec 2017, 00:27
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Difficulty:

25% (medium)

Question Stats:

86% (01:33) correct 14% (02:21) wrong based on 34 sessions

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The volume of a cylindrical tank is directly proportional to the height and the square of the radius of the tank. If a certain tank with a radius of 10 centimeters has a volume of 20,000 cubic centimeters, what is the volume, in cubic centimeters, of a tank of the same height with a radius of 15 centimeters?

(A) 300,000
(B) 45,000
(C) 30,000
(D) 15,000
(E) 4,500

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Joined: 24 Nov 2016
Posts: 152
Re: The volume of a cylindrical tank is directly proportional to the heigh  [#permalink]

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10 Dec 2017, 03:46
Bunuel wrote:
The volume of a cylindrical tank is directly proportional to the height and the square of the radius of the tank. If a certain tank with a radius of 10 centimeters has a volume of 20,000 cubic centimeters, what is the volume, in cubic centimeters, of a tank of the same height with a radius of 15 centimeters?

(A) 300,000
(B) 45,000
(C) 30,000
(D) 15,000
(E) 4,500

$$\frac{10cm}{20,000cm^3}=\frac{15cm}{x}, 10cm*x=20,000cm^3*15, x=30,000cm^3$$

Intern
Joined: 27 Sep 2015
Posts: 5
The volume of a cylindrical tank is directly proportional to the heigh  [#permalink]

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10 Dec 2017, 04:06
V ∝ h*r^2 , where v= volume, h= height and r= radius of a cylinder .
So V= (hr^2 )k where k= constant .

So V1= 20000 cm^3= {h(10 cm)^2}k
V2= {h(15 cm)^2 }k

Dividing V1 by V2 we get,

V1/V2= (10/15)^2,
20000/V2= (2/3)^2=4/9,
So V2= 45000 cm^3,

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Joined: 22 May 2016
Posts: 2222
The volume of a cylindrical tank is directly proportional to the heigh  [#permalink]

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10 Dec 2017, 10:44
Bunuel wrote:
The volume of a cylindrical tank is directly proportional to the height and the square of the radius of the tank. If a certain tank with a radius of 10 centimeters has a volume of 20,000 cubic centimeters, what is the volume, in cubic centimeters, of a tank of the same height with a radius of 15 centimeters?

(A) 300,000
(B) 45,000
(C) 30,000
(D) 15,000
(E) 4,500

All measures are in centimeters; units omitted.

Direct proportion: When $$y$$ increases, $$x$$ increases

$$y = kx$$*, and $$\frac{y}{x}=k$$
$$k$$ is the constant of proportionality: it does not change

Find $$k$$ from the first scenario, and use $$k$$ to find volume in the second scenario

Scenario 1 - find $$k$$
The volume of a cylindrical tank is directly proportional to the height and the square of the radius of the tank

$$V = (k)(h)(r^2)$$ , and

$$\frac{V}{(h)(r^2)} = k$$

Height does not change. Remove it.
$$V_1 = 20,000$$
$$r_1 = 10$$

$$\frac{V_1}{(r_1)^2}= k$$

$$\frac{20,000}{(100)} = 200 = k$$

Scenario 2 - Use the same formula; and $$k$$; and the given new radius to find new volume, $$V_2$$

$$k = 200$$
$$r_2 = 15$$
New volume, $$V_2$$?

$$\frac{V_2}{(r_2)^2} = k$$

$$\frac{V_2}{225} = 200$$

$$V_2 = (225)(200) = 45,000$$

*Sometimes written $$y ∝ x$$
The volume of a cylindrical tank is directly proportional to the heigh &nbs [#permalink] 10 Dec 2017, 10:44
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