Cube

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N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Fri Dec 10, 2010 12:03 am

I don't understand this question:

Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, rectangular-shaped pan. The base of the pan has inside dimensions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep. If the volume of the solid lead is approximately the same as the volume of the molted lead, approximately how many centimeters deep is the melted lead in the pan?

a. 2.5
b. 3
c. 5
d. 7.5
e. 9

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Source: Beat The GMAT — Problem Solving | Fri Dec 10, 2010 12:03 am

goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Fri Dec 10, 2010 1:10 am

N:Dure wrote:I don't understand this question:

Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, rectangular-shaped pan. The base of the pan has inside dimensions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep. If the volume of the solid lead is approximately the same as the volume of the molted lead, approximately how many centimeters deep is the melted lead in the pan?

a. 2.5
b. 3
c. 5
d. 7.5
e. 9

Volume of one Cube is 10 * 10 * 10 = 1000 cm^3

Total Volume is 3000 Cm^3

Base of Rectangular Cuboid is 20 and length of Rectangular Cuboid is 30

20 * 30 * x = 3000 , x = 5

approximately how many centimeters deep is the melted lead in the pan?

This line confused me a bit, But i would still like to bet on 5

What's is the OA?

Saurabh Goyal
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shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

by shovan85 » Fri Dec 10, 2010 1:35 am

N:Dure wrote:I don't understand this question:

Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, rectangular-shaped pan. The base of the pan has inside dimensions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep. If the volume of the solid lead is approximately the same as the volume of the molted lead, approximately how many centimeters deep is the melted lead in the pan?

a. 2.5
b. 3
c. 5
d. 7.5
e. 9

Volume of 3 cubes = 3 * (10)^3 = 3000 cubic cm

This much lead is to be melted.

The Volume of the rectangular Pan = 20*30*15 = 9000 cubic cm

Now question says "the volume of the solid lead is approximately the same as the volume of the molted lead"

This means the volume of the molten part of the cube is half of the total volume of the 3 cubes.

Thus, Vol melted = 3000/2 = 1500 cubiccm

This much volume is spraded on the bese of the rectangular pan of 20*30 = 600 sqr cm.

Thus the required height (deep) = 1500/600 = 5/2 = 2.5CM

PICK A

If the problem is Easy Respect it, if the problem is tough Attack it

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Dec 10, 2010 5:05 am

N:Dure wrote:Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, rectangular-shaped pan. The base of the pan has inside dimensions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep. If the volume of the solid lead is approximately the same as the volume of the melted lead, approximately how many centimeters deep is the melted lead in the pan?
a. 2.5
b. 3
c. 5
d. 7.5
e. 9

Total volume of the three lead cubes = 3*(10)*(10)*(10) cc = 3000 cc
As "volume of the solid lead is approximately the same as the volume of the melted lead", the volume of melted lead is also 3000 cc.

Now the base of the pan has inside dimensions of 20 cm by 30 cm => Area of the base of the pan = (20)*(30) = 600 cmÂ²

Say the depth of the melted lead is h, then (600)*(h) = 3000 => h = 5

The correct answer is C.

shovan85 wrote:Now question says "the volume of the solid lead is approximately the same as the volume of the molted lead"

This means the volume of the molten part of the cube is half of the total volume of the 3 cubes.

What is the logic behind such interpretation?

Rahul Lakhani
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shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

by shovan85 » Fri Dec 10, 2010 5:23 am

Rahul@gurome wrote:
shovan85 wrote:Now question says "the volume of the solid lead is approximately the same as the volume of the molted lead"

This means the volume of the molten part of the cube is half of the total volume of the 3 cubes.
What is the logic behind such interpretation?

I thought the 3 cubes are melting. Also the question says in the first line that "are melted together in a level," . So I thought by the line "the volume of the solid lead is approximately the same as the volume of the molted lead" is trying to say "the volume of the molten part of the cube is half of the total volume of the 3 cubes".

You know me as usual unnecessary digging into the problem. Luckily I get saved by Options but not this time

If the problem is Easy Respect it, if the problem is tough Attack it

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Dec 10, 2010 10:55 am

shovan85 wrote:I thought the 3 cubes are melting. Also the question says in the first line that "are melted together in a level," . So I thought by the line "the volume of the solid lead is approximately the same as the volume of the molted lead" is trying to say "the volume of the molten part of the cube is half of the total volume of the 3 cubes".

You know me as usual unnecessary digging into the problem. Luckily I get saved by Options but not this time

Don't go so much deep!

If that was the case, it would have been a problem on application of calculus!

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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