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A truck driver wants to load as many identical cylindrical canisters

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Bunuel
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A truck driver wants to load as many identical cylindrical canisters [#permalink] New post   30 Aug 2016, 05:13
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A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3-meter × 4-meter × 9-meter storage space of his truck. How many canisters can he load into the truck?

(1) Each canister has a volume of 62, 500π cubic centimeters.
(2) The height of each canister is four times the radius.
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C
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Re: A truck driver wants to load as many identical cylindrical canisters [#permalink] New post   30 Aug 2016, 07:42
Bunuel wrote:
A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3-meter × 4-meter × 9-meter storage space of his truck. How many canisters can he load into the truck?

(1) Each canister has a volume of 62, 500π cubic centimeters.
(2) The height of each canister is four times the radius.



1 m = 100 cm
\(1 m^3 = 10^6 cm^3\)
We need to know what's the \(r\) and \(h\) to find whether how many canisters can be loaded

Consider 1) Volume of cylinder = \(\pi * r^2 * h\), there can be multiple values of \(r\) and \(h\) for the given volume. Eliminate A and D
Consider 2) \(h = 4r\), Not sufficient, since multiple values can exist, Eliminate B

Consider 1) and 2) together, \(\pi * r^2 * 4 *4 = 62,500\pi\), this solves for \(r\) and hence \(h\). So C is the answer.
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Re: A truck driver wants to load as many identical cylindrical canisters [#permalink] New post   30 Aug 2016, 20:08
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Bunuel wrote:
A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3-meter × 4-meter × 9-meter storage space of his truck. How many canisters can he load into the truck?

(1) Each canister has a volume of 62, 500π cubic centimeters.
(2) The height of each canister is four times the radius.


Question : many canisters can he load into the truck?

Note: To find the number of cannisters we require
1) Dimensions of Cylinder i.e. Radius and Height of cylindrical canister
2) Dimensions of Truck

Statement 1: Each canister has a volume of 62, 500π cubic centimeters
Dimensions of cylinder are unknown hence
NOT SUFFICIENT

Statement 2: The height of each canister is four times the radius
Ratio between dimensions of cylinder is given but Dimensions of cylinder in actual are unknown hence
NOT SUFFICIENT

Combining the two statements
h = 4r
Volume = π*r^2*h = π*r^2*(4r) = 62, 500π
this gives us radius and also the height
Now we can divide each dimension of base of truck with radius of cylinder to find the number of cylinders than can be rest on base of truck.
SUFFICIENT

Answer: Option C
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Re: A truck driver wants to load as many identical cylindrical canisters [#permalink] New post   23 Jan 2017, 23:24
GMATinsight wrote:
Bunuel wrote:
A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3-meter × 4-meter × 9-meter storage space of his truck. How many canisters can he load into the truck?

(1) Each canister has a volume of 62, 500π cubic centimeters.
(2) The height of each canister is four times the radius.


Question : many canisters can he load into the truck?

Note: To find the number of cannisters we require
1) Dimensions of Cylinder i.e. Radius and Height of cylindrical canister
2) Dimensions of Truck

Statement 1: Each canister has a volume of 62, 500π cubic centimeters
Dimensions of cylinder are unknown hence
NOT SUFFICIENT

Statement 2: The height of each canister is four times the radius
Ratio between dimensions of cylinder is given but Dimensions of cylinder in actual are unknown hence
NOT SUFFICIENT

Combining the two statements
h = 4r
Volume = π*r^2*h = π*r^2*(4r) = 62, 500π
this gives us radius and also the height
Now we can divide each dimension of base of truck with radius of cylinder to find the number of cylinders than can be rest on base of truck.
SUFFICIENT

Answer: Option C


HI, I have a doubt here.
Using both statements, we get r=25cm and h=100cm. And the dimensions of the truck are 300cm*400cm*900cm.
So wont the number of cylinders differ if we consider 300cm*400cm as the base and 900cm as the height OR 300cm*900cm as the base and 400cm as the height OR 400cm*900cm as the base and 300cm as the height?
So should t the answer be (E) ?
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Re: A truck driver wants to load as many identical cylindrical canisters [#permalink] New post   23 Jan 2017, 23:41
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ishan92 wrote:
GMATinsight wrote:
Bunuel wrote:
A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3-meter × 4-meter × 9-meter storage space of his truck. How many canisters can he load into the truck?

(1) Each canister has a volume of 62, 500π cubic centimeters.
(2) The height of each canister is four times the radius.


Question : many canisters can he load into the truck?

Note: To find the number of cannisters we require
1) Dimensions of Cylinder i.e. Radius and Height of cylindrical canister
2) Dimensions of Truck

Statement 1: Each canister has a volume of 62, 500π cubic centimeters
Dimensions of cylinder are unknown hence
NOT SUFFICIENT

Statement 2: The height of each canister is four times the radius
Ratio between dimensions of cylinder is given but Dimensions of cylinder in actual are unknown hence
NOT SUFFICIENT

Combining the two statements
h = 4r
Volume = π*r^2*h = π*r^2*(4r) = 62, 500π
this gives us radius and also the height
Now we can divide each dimension of base of truck with radius of cylinder to find the number of cylinders than can be rest on base of truck.
SUFFICIENT

Answer: Option C


HI, I have a doubt here.
Using both statements, we get r=25cm and h=100cm. And the dimensions of the truck are 300cm*400cm*900cm.
So wont the number of cylinders differ if we consider 300cm*400cm as the base and 900cm as the height OR 300cm*900cm as the base and 400cm as the height OR 400cm*900cm as the base and 300cm as the height?
So should t the answer be (E) ?


Hi ishan,

They are asking for CAN. This will mean maximum, as if it can carry say 100 boxes, it can always carry 1 box to all 100 boxes..

Had the Q asked :-
The vehicle is full and how many is it carrying. Then it would be E
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Re: A truck driver wants to load as many identical cylindrical canisters [#permalink] New post   11 Dec 2020, 06:12
Bunuel wrote:
A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3-meter × 4-meter × 9-meter storage space of his truck. How many canisters can he load into the truck?

(1) Each canister has a volume of 62, 500π cubic centimeters.
(2) The height of each canister is four times the radius.



Why not just divide the overall load of truck (960mp)to 62 500 ? We can understand how many canisters may be fit in.
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Re: A truck driver wants to load as many identical cylindrical canisters [#permalink] New post   01 Oct 2023, 09:25
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Re: A truck driver wants to load as many identical cylindrical canisters [#permalink]
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