A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving

Question: A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylinder that can be placed inside the box?

1. 180\(\pi\)
2. 200\(\pi\)
3. 300\(\pi\)
4. 320\(\pi\)
5. 450\(\pi\)

‘A rectangular box has dimensions 12*10*8 inches’ - is the topic from the GMAT Quantitative problem set. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Approach Solution 1:
Dimensions of the box are 12*10*8 inches if radius of a cylinder is 6 then its diameter is 12 and it won't fit on any face of a box. For example it can not fit on 12*10 face of the box since diameter=12>10=side.
Complete solution:
A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylcinder that can be placed inside the box?
\(Volume_{cylinder}\)=\(\pi\)\(r^2\)h
If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4
Volume
= \(\pi\)*\(4^2\)*12
=192\(\pi\)
If the cylinder is placed on 8*12 face then it's maximum radius is 8/2=4
Volume
= \(\pi\)*\(4^2\)*10
=160\(\pi\)
If the cylinder is placed on 10*12 face then it's maximum radius is 10/2=5
Volume
= \(\pi\)*\(5^2\)*8
=200\(\pi\)
So, the maximum volume is for 200\(\pi\).
Hence, B is the correct answer.

Correct Answer: B

Approach Solution 2:

Candidates must Remember that the base of the cylinder is a circle
r is constant around the circle, so the base can completely fit in a square, not a rectangle. Therefore, they will not be able to use the entire space in the base of
the rectangular box.
the volume of a cylinder is pi * r^2 * h
We must select largest possible r such that the dimensions of the rectangular base allow maximum value or r
We would want to maximize r more than h because r is squared here
so, select bases 10 and 12 allowing a maximum value of r = 5
volume of cylinder: 25 pi * 8 = 200 pi
to check, think if 8 is one of the dimensions of the base, r = 4
volume of cyclinder: 16 pi * (either 10 or 12 ) = 160 pi or 192 pi
not maximum volume
Hence, B is the correct answer.

Correct Answer: B

Approach Solution 3:

this problem can be solved using formula directly. This is a easy and time saving method.

The volume of cylinder is pi * r^2 * h
So, the largest value if r or h are two of the largest value used.
Considering r = 12, h = 10,

we get, v = pi*36*10 = 360pi
And Considering r = 10, h = 12,

we get, v = pi*25*12 = 300pi.

Considering the value of r = 5, h=8
volume of cylinder: 25 pi * 8 = 200 pi
Correct Answer: B

Suggested GMAT Problem Solving Questions

• Properties of Circle GMAT Problem Solving 
• If 10, 12 and ‘x’ are sides of an acute angled triangle, GMAT Problem Solving 
• Assume that all 7-digit numbers that do not begin with 0 or 1 are valid phone numbers GMAT Problem Solving 
• What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Problem Solving 
• The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5 GMAT Problem Solving 
• The maximum mark in an examination is 100 and the minimum is 0 GMAT Problem Solving  
• A rectangular box has dimensions 12*10*8 inches GMAT Problem Solving 
• A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving 
• If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day GMAT Problem Solving 
• If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal? GMAT Problem Solving 
• How many terminating zeroes does 200! have? GMAT Problem Solving
• For How Many Values of k is 12^12 the Least Common Multiple GMAT Problem Solving
• Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 GMAT Problem Solving 
• A certain sum of money is divided among A, B and C such that A gets one-third GMAT Problem Solving
• A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its speed is v miles per hour GMAT Problem Solving 
• What is the value of x? (1) x^2 – 5 x + 6 = 0 (2) x > 0 GMAT Problem Solving 
• How many even divisors of 1600 are not multiples of 16? GMAT Problem Solving 
• How many 5 digit (digit = 0 - 9) zip codes can exist in which at least one digit is repeated? GMAT Problem Solving 
• Is Square Root = Always Positive? GMAT Problem Solving