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Tanks A and B are each in the shape of a right circular cylinder. The

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Bunuel
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Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   06 Feb 2020, 09:18
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Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%


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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   07 Feb 2020, 02:47
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Bunuel wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

A. 75%
B. 80%
C. 100%
D. 120%
E. 125%


Heights of tank1 and tank2 are in the ratio 10:8 = 5 / 4
Circumference (which means radius too) is in the ratio 8 : 10 = 4 / 5

Volumes will be in the ratio r^2*h so ratio will be \(\frac{5*4^2 }{ 4*5^2} = \frac{4}{5}\)
So Capacity of tank A is 4/5*100 = 80% of capacity of tank B.
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   06 Feb 2020, 09:28
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Bunuel wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

A. 75%
B. 80%
C. 100%
D. 120%
E. 125%


For the question we are looking for a ratio, is it possible to use ratios only to find ratios. The formula for the volume of a cylinder is \(V = \pi * r^2 * h \). Focus on the variables in the formula, we only need to compare their radius squared and height. The ratio of radii is 8:10. The ratio of heights is 10:8. Then the ratio of the volumes is \((\frac{8}{10})^2 * \frac{10}{8} = 8/10 = 80%\)

Ans: B
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   07 Feb 2020, 01:08
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Bunuel wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

A. 75%
B. 80%
C. 100%
D. 120%
E. 125%

Solution


    • Let us assume that the radii of tank A and tank B are \( r_1 \) and \(r_2 \) respectively.
    • Now, \(2*π*r_1 = 8\) and \(2*π*r_2 = 10\)
    • Dividing circumference of tank, A by that of tank B we have:
      o \(\frac{2*π*r_1}{2*π*r_2 }= \frac{8 }{ 10} \)
         Or, \(\frac{r_1}{r_2} = \frac{4}{5} …………Eq.(i)\)
    • Now, volume of tank A \(= π*r_1^2*height= π*r_1*10 \)
    • And volume of tank B\( = π*r_2^2*height = π*r_2*8\)
    • Hence, Required percentage \(= \frac{π*r_1^2*10}{ π*r_2^2*8} *100⟹(\frac{r_1}{r_2}) ^2 * \frac{5}{4}*100 \)
Substituting the value of \(\frac{r_1}{r_2}\) from Eq. (1) into the above equation, we get:
Required percentage \(= \frac{16}{25}*\frac{5}{4}*100 = 80 \)%
Thus, the correct answer is Option B.
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   Updated on: 20 Apr 2020, 12:28
for tank A,
h=10m
circumference=pi(2)r=8
r=4/pi
volume of tank=pi(r^2)h
=pi*16/pi^2*10=32/pi m^3

for tank B,
h=8m
circumference=pi(2)r=10
r=5/pi
volume of tank=pi(r^2)h
=pi*5/pi^2*8=40/pi m^3

The capacity of tank A is what percent of the capacity of tank B=(32/pi)/(40/pi)*100=80%
Answer is 80%

Originally posted by SameerGupta2001 on 20 Apr 2020, 12:18.
Last edited by SameerGupta2001 on 20 Apr 2020, 12:28, edited 1 time in total.
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   20 Apr 2020, 12:20
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IOC is B 80%
Circumference of cylinder A = 2πr=8
R=4/π
Volume/capacity of tank A = πr^2h
π*4/π*4/π*10 = 160/π ------(1)

Circumference of cylinder B = 2πr=10
R=6/π
Volume/capacity of tank A = πr^2h
π*5/π*5/π*18 = 200/π ------(2)

Let Tank A capacity is X Percentage of tank B
200/π*X/100=160/π
16000/200=80
X=80%

IOC is 80% (B)

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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   21 Apr 2020, 10:47
gmatt1476 wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%


PS94530.02


for tank a ;
h= 10 ;
2 * pi *r = 8
pi * r= 4 & r = 4/pi
for tank b
h= 8
2*pi*r = 10
pi*r = 5 an r = 5/pi
area of tank a /area of tank b = 4*4/pi * 10 / 8 * 5/pi * 5
we get 80 %
OPTION B
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   29 Apr 2020, 17:12
gmatt1476 wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%


PS94530.02


Capacity of Tank A as a percent of the capacity of tank B = Capacity (Volume) of Tank A / Capacity (Volume) of Tank B *100

Since both are right circular cylinder (Volume = pi . r^2. h)

We have the height for both tanks however we need to figure out the radius of each of these. In order to find out the radius we will need to use the information of circumference.

Length of Circumference for Tank A = 2 . Pi. R
8 = 2. Pi. R
R= 4/Pi

Similarly Length of Circumference for Tank B = 2 . Pi. R
10 = 2 Pi R
R = 5 / Pi

Now Volume of Tank A / Vol of Tank B =\( (Pi (4/pi)^2. 10 )/ (Pi (5/pi)^2 .8)\)

After Cancelling out it comes out to

4/5 = 80%
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   01 May 2020, 15:41
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gmatt1476 wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%


PS94530.02


Recall that the circumference of a circle with radius r is C = 2πr. The volume of a cylinder with height h and radius r is V = πr^2*h. Since the height of tank A is 10 and the radius is 8/(2π) = 4/π, the volume of tank A is π(4/π)^2*10 = π(16/π^2)*10 = 160/π. Likewise, since the height of tank B is 8 and the radius is 10/(2π) = 5/π, the volume of tank B is π(5/π)^2*8 = π(25/π^2)*8 = 200/π.

Therefore, the volume of tank A is (160/π) / (200/π) x 100 = 160/200 x 100 = 80 percent of that of tank B.

Answer: B
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   07 May 2020, 10:54
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gmatt1476 wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%

PS94530.02

Let's just deal in ratios.
Ratio of radius of Tank A to that of Tank B, \(\frac{r_A}{r_B}\) = Ratio of circumference of Tank A to that of Tank B = \(\frac{8}{10} = \frac{4}{5}\)
Ratio of height of Tank A to that of Tank B, \(\frac{h_A}{h_B}\) = \(\frac{10}{8} = \frac{5}{4}\)

Ratio of capacity of Tank A to that of Tank B = \(\frac{π*r_A^2*h_A}{π*r_B^2*h_B} = (\frac{r_A}{r_B})^2*\frac{h_A}{h_B} = \frac{4}{5}*\frac{4}{5}*\frac{5}{4} = \frac{4}{5}\)

Answer B.
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Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   28 Jun 2020, 00:31
Soln:

Tank A - H=10 and C= 8
Tank B- h=8 and c = 10

Vol of cylinder =Pi * r^2 h

We need to know Capacity of Tank A=x % of Capacity of Tank B

So x/100 =Capacity of Tank A/Capacity of Tank B
= Pi* R^2*H/ Pi * r^2* h
= R^2*H/ r^2 *h

Basically to find x we need ratio of radius and ht of Tank A and Tank B

C/c=2Pi* R/ 2Pi*r=8/10

R/r=8/10

H/h=10/8

Putting ratio of radius and ht in ratio of capacity formula derived above

x/100=R^2*H/ r^2 *h
=8*8*10/ 10*10*8

x/100 = 80/100

Therefore x =80%

And Choice B

Hope it helps :thumbsup:
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Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   12 Feb 2021, 02:23
Top Contributor
[b]SOLUTION:
[/b]
A NEW OG 2021 QUESTION

Volume of Tank A (VA) = pi * (R1)^2 * H1

Volume of Tank B (VB) = pi * (R2)^2 * H2

Circumference (A)=8
=> 2*pi* R1 =8=> R1 = 8/2*pi and similarly R2 = 10/2*pi

Substitute these values in VA/VB to have

VA/VB

= (R1)^2 * H1/ (R2^2 * H2)

= 8^2 * 10 / (10)^ 2 * 8

= 8/10

=> VA/VB =8/10 = >VA is 80% of VB (OPTION B)

Hope this helps :thumbsup:
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   24 Mar 2021, 09:01
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ScottTargetTestPrep wrote:
gmatt1476 wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%


PS94530.02


Recall that the circumference of a circle with radius r is C = 2πr. The volume of a cylinder with height h and radius r is V = πr^2*h. Since the height of tank A is 10 and the radius is 8/(2π) = 4/π, the volume of tank A is π(4/π)^2*10 = π(16/π^2)*10 = 160/π. Likewise, since the height of tank B is 8 and the radius is 10/(2π) = 5/π, the volume of tank B is π(5/π)^2*8 = π(25/π^2)*8 = 200/π.

Therefore, the volume of tank A is (160/π) / (200/π) x 100 = 160/200 x 100 = 80 percent of that of tank B.

Answer: B


Is the formula of circumference of a cylinder 2πr, probably not. then how can we say 2πr=8?
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   19 Apr 2021, 04:31
Isn't curved / lateral surface area of a cylinder 2(pie)(r)(h)?
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   25 May 2021, 07:10
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Bunuel wrote:
Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%


PS94530.02


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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   03 Mar 2022, 06:24
i also did the same mistake
i took circumference as 2(pi)rh
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   19 Oct 2022, 08:05
Hi Experts, Bunuel chetan2u

Although my answer was correct for this question but I want to understand one thing, which probably everybody in this question thread has written wrong.

Don't you guys think that Circumference of cylinder is == 2 * 2*pi*r

I understand there will be no impact in the answer but I just want to know whether my thought process is correct or not.

Thanks for your time and reply.
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   19 Oct 2022, 08:53
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760Abhi wrote:
Hi Experts, Bunuel chetan2u

Although my answer was correct for this question but I want to understand one thing, which probably everybody in this question thread has written wrong.

Don't you guys think that Circumference of cylinder is == 2 * 2*pi*r

I understand there will be no impact in the answer but I just want to know whether my thought process is correct or not.

Thanks for your time and reply.



Circumference of any tank etc of negligible thickness will be \(2*\pi r\)

But if you have a thick material, then you will have inner and outer circumference. Both will be different but not 2* \(2*\pi r\)
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Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   19 Oct 2022, 11:04
chetan2u wrote:
760Abhi wrote:
Hi Experts, Bunuel chetan2u

Although my answer was correct for this question but I want to understand one thing, which probably everybody in this question thread has written wrong.

Don't you guys think that Circumference of cylinder is == 2 * 2*pi*r

I understand there will be no impact in the answer but I just want to know whether my thought process is correct or not.

Thanks for your time and reply.



Circumference of any tank etc of negligible thickness will be \(2*\pi r\)

But if you have a thick material, then you will have inner and outer circumference. Both will be different but not 2* \(2*\pi r\)


Hi chetan2u

Thanks for your reply.

If it's a tank then I am assuming it to be in a cylindrical shape (Let's suppose negligible thickness) and then we have two circles i.e. (at the bottom & at the top) Hence Total circumference will be == circumference of top + circumference of bottom == 2* 2*pi*r

I am not able to find a logic gap in my reasoning, please help.
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink] New post   24 Oct 2023, 05:34
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Re: Tanks A and B are each in the shape of a right circular cylinder. The [#permalink]
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