An interior designer has the contract for decorating the atrium of a b

Question

An interior designer has the contract for decorating the atrium of a business school. As part of the design, he intends to install a solid globe-like sphere in the middle of the atrium. The cost involved in installing the sphere is $70 per cubic feet of metal use and an extra 50% cost for designing, assembly, and labor charges. He is considering two sizes of the globe, with diameters 7 feet and 10 feet respectively. The volume of a sphere is  \frac{4}{3} π r^3 , where r is the radius of the sphere.
In the table, select the values that represent the approximate costs of installing the globes with diameters 7 feet and 10 feet respectively. Make only two selections, one in each column.

architkap · Answer

can someone please let me know if this kind of question is still a part of the syllabus for DI?

Vivek1707 · Answer

Hi  architkap

Even though geometry is not part of the syllabus, some application based questions can still be asked.

There are a few simlar quesitons in the OG and official prep material.

Some are even asked in the Official GMAT mock tests.

Edskore · Answer

Ok this one is fun because of the units mismatch trap buried in it. Two-part Analysis loves doing this, giving you a diameter and hoping you plug it straight into the sphere volume formula without converting to radius first.

1. Volume of a sphere is (4/3)πr^3, and you're given diameters, not radii. For the 7 ft globe, r = 3.5, so r^3 = 42.875. Volume comes out to about 179.6 cubic feet.

2. Metal cost is $70 per cubic foot, so that's 179.6 × 70, roughly $12,570 just for the metal.

3. Here's the part people skip when they're rushing, there's an extra 50% tacked on for design, assembly, and labor. So the real total is 12,570 × 1.5, which lands you around $18,900, close enough to the $19,000 answer.

4. Same process for the 10 ft globe. r = 5, r^3 = 125, volume is about 523.6 cubic feet.

5. Metal cost is 523.6 × 70, around $36,650. Add the 50% markup and you get roughly $54,980, which rounds to $55,000.

I got burned by almost the exact same trap on a practice test, used the diameter as the radius and got an answer that was 8x too big (since it's cubed, that error compounds fast). If your answer choice is way off from everything listed, that's usually your first clue you mixed up r and d.

Takeaway: with sphere or cylinder volume questions, convert diameter to radius before you touch the formula, and always check whether there's a second cost layer hiding in the word problem before you lock in an answer.

suntprovident · Answer

Why is the difficulty 85% ? Aren't you allowed to use calculators in DI or am I missing something

Diameter 7 feet	Diameter 10 feet	Installation cost
		$11000
		$19000
		$55000
		$150000
		$440000

An interior designer has the contract for decorating the atrium of a b

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GMAT Two-part Analysis (TPA) Questions

An interior designer has the contract for decorating the atrium of a b

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