Problem Solving

A closed cylindrical tank contains 36Ï€ cubic feet of
water and is filled to half its capacity. When the tank
is placed upright on its circular base on level ground,
the height of the water in the tank is 4 feet. When the
tank is placed on its side on level ground, what is the
height, in feet, of the surface of the water above the
ground?

I did not quite understand the explanation given in teh book. Any thoughts on this please.

becnil wrote:A closed cylindrical tank contains 36Ï€ cubic feet of
water and is filled to half its capacity. When the tank
is placed upright on its circular base on level ground,
the height of the water in the tank is 4 feet. When the
tank is placed on its side on level ground, what is the
height, in feet, of the surface of the water above the
ground?

I did not quite understand the explanation given in teh book. Any thoughts on this please.

volume of cyl=pi r^2 H
now V=1/2(volume)=pi r^2 H/2=36

from here we r
now when the cylinder is laid down along the side
the height will be= dia of circlular base
since its half filled H=d/2=r

HTH

becnil wrote:A closed cylindrical tank contains 36Ï€ cubic feet of
water and is filled to half its capacity. When the tank
is placed upright on its circular base on level ground,
the height of the water in the tank is 4 feet. When the
tank is placed on its side on level ground, what is the
height, in feet, of the surface of the water above the
ground?

I did not quite understand the explanation given in teh book. Any thoughts on this please.

The volume of cylindrical tank = π *r^2*h

now h = 4
Volume = 36Ï€

r^2 = Volume/Ï€*h = 36Ï€/4Ï€ = 9
r= 3 feet

The tank has a height of 8 feet (it is mentioned that tank is only half filled) and it is half full
So if it is kept on sides, it will be filled till half of the diameter

Diameter = 6 feet, the tank will be filled till 3 feet

Thank You Ajith and The Phoenix

why is the height = 4?

i thought the height is 8, since the height of the water is the tank is 4 feet when the tank is filled to half its capacity...

thx

Its simple...

What given Volume = 36

Height = 4ft

Volume = Pi* r2 * h
36 = Pi*r2 * 4
r2 =9

r = 3

So the radius is 3 which means the diameter is 6.

This is what the ques asked.

why is the height = 4?

i thought the height is 8, since the height of the water is the tank is 4 feet when the tank is filled to half its capacity:

r^2 * pi * 8 = 36 * pi

could anybody explain plz?

Fractal wrote:why is the height = 4?

i thought the height is 8, since the height of the water is the tank is 4 feet when the tank is filled to half its capacity:

r^2 * pi * 8 = 36 * pi

could anybody explain plz?

ah i think i got it now! the phrase "... is filled to half its capacity" is needless to calculate r. the tank is half full, and this equals 36 * pi

i misinterpreted the text...

In my version of the book, the question is given as:

A closed cylindrical tank contains 36Ï€ cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Note the height of the water has changed.

This is how I attempted to solve the problem:

V = h x πr2

Total volume of container, since it is half full, would be 72Ï€

72π = 4 x πr2
18 = r2
square root 18 = r

Therefore, when the tank is placed on its side, shouldn't the height of the water be the square root of 18?

A closed cylindrical tank contains 36Ï€ cubic feet of
water and is filled to half its capacity. When the tank
is placed upright on its circular base on level ground,
the height of the water in the tank is 2 feet. When the
tank is placed on its side on level ground, what is the
height, in feet, of the surface of the water above the
ground?

I did not quite understand the explanation given in teh book. Any thoughts on this please.

my book says the same thing, and I was confused as well!

Rainy wrote:In my version of the book, the question is given as:

A closed cylindrical tank contains 36Ï€ cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Note the height of the water has changed.

This is how I attempted to solve the problem:

V = h x πr2

Total volume of container, since it is half full, would be 72Ï€

72π = 4 x πr2
18 = r2
square root 18 = r

Therefore, when the tank is placed on its side, shouldn't the height of the water be the square root of 18?

I have this same issue with the problem. The problem CLEARLY states that "A closed cylindrical tank contains 36Ï€ cubic feet of water" and you are told that the tank is only half full. So that would mean that the total volume of the tank is 72Ï€, but no, they say that the volume is 36Ï€ and thus the volume of the water within the tank is 18Ï€.

They should have stated that the volume of the tank was 36Ï€, not that the volume of the water within the tank is 36Ï€.

I also got this one "wrong" but in my opinion it's a flaw in the question.

For the 13th edition of the OG the question states a height of the water level of 2 feet. This is wrong and should be 4 feet.