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catinabox
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26 Aug 2024, 09:33
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Rod 1 Production Cost: $70
Rod 2 Production Cost: $60
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
83% (02:39) correct
17%
(02:48)
wrong
based on 199
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A factory produces two types of cylindrical metal rods, and the production cost is based on the volume of the material used. The volume V of a cylinder is calculated using the formula \(Pi * R^2 * H\), where R is the radius and H is the height. Pi = 3.14 (approximately)
If the production cost is $15 per cubic meter, and the first rod has a radius of 0.5 meters and a height of 6 meters, while the second rod has a radius of 0.4 meters and a height of 8 meters, what is the total production cost for one of each rod type?
Make only two selections, one in each column.
If the production cost is $15 per cubic meter, and the first rod has a radius of 0.5 meters and a height of 6 meters, while the second rod has a radius of 0.4 meters and a height of 8 meters, what is the total production cost for one of each rod type?
Make only two selections, one in each column.
| Rod 1 Production Cost | Rod 2 Production Cost | |
| $50 | ||
| $60 | ||
| $70 | ||
| $80 | ||
| $90 |
ShowHide Answer
Official Answer
Rod 1 Production Cost: $70
Rod 2 Production Cost: $60
27 Aug 2024, 06:26
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There’s actually a lot to calculate here I mean pi is 22/7 I don’t think that it’s possible to be added in the official gmat cause it’ll require quite a significant amount of calculations
27 Aug 2024, 06:40
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yazadsarkari
Official Solution:
Notice how the answers in the options are spaced apart by $10, which means you have significant leeway to approximate your calculations.
You can consider pi = 3.14 or ~3 in this case.
Rod 1:
Volume for the first rod = \(Pi * R^2 * H = 3 * 0.5^2* 6 = .25* 18 = 4.5\)
Production cost for the first rod = \(4.5 * 15 = 67.5\)
Remember that we've lowered the approx value of pi from 3.14 to 3, therefore, the final answer must be slightly higher than 67.5 => 70 must be correct.
Rod 2:
Volume for the second rod = \(3 * 0.4^2 * 8 = 24 * 0.16\)
Production cost for the second rod =\(15 * 24 * 0.16 = 24 * 2.4 = 57.6\)
Again, the closest value slightly greater than 57.6 is 60.
