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# The City Opera House is expanding. Currently the city block containing

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Senior Manager
Joined: 02 Jan 2017
Posts: 307
The City Opera House is expanding. Currently the city block containing  [#permalink]

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02 Mar 2017, 21:16
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Difficulty:

25% (medium)

Question Stats:

80% (02:08) correct 20% (02:32) wrong based on 78 sessions

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The City Opera House is expanding. Currently the city block containing the opera house is rectangular-shaped with a total volume of 9600 feet. If the expanded Opera House is 2.5 times as long, wide, and deep as the original building, what would the new volume be?

A. 24,000
B. 60,000
C. 72,000
D. 150,000
E. 245,000
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Posts: 9125
Location: Pune, India
Re: The City Opera House is expanding. Currently the city block containing  [#permalink]

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02 Mar 2017, 22:43
2
vikasp99 wrote:
The City Opera House is expanding. Currently the city block containing the opera house is rectangular-shaped with a total volume of 9600 feet. If the expanded Opera House is 2.5 times as long, wide, and deep as the original building, what would the new volume be?

A. 24,000
B. 60,000
C. 72,000
D. 150,000
E. 245,000

Use approximation. The current volume is 9600 which is about 10,000 cubic feet.

If length, width and height are each made 2.5 times, the overall volume will become 2.5*2.5*2.5 = 15.625 times the previous volume.

This means the new volume will be about 150,000.

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Re: The City Opera House is expanding. Currently the city block containing  [#permalink]

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03 Mar 2017, 00:23
1
vikasp99 wrote:
The City Opera House is expanding. Currently the city block containing the opera house is rectangular-shaped with a total volume of 9600 feet. If the expanded Opera House is 2.5 times as long, wide, and deep as the original building, what would the new volume be?

A. 24,000
B. 60,000
C. 72,000
D. 150,000
E. 245,000

l*b*h = 9600

Expanded Opera House is 2.5 times as long, wide, and deep as the original building
2.5l * 2.5b * 2.5h
= $$2.5^3$$ * l*b*h
= $$2.5^3$$ * 9600
= 150000

Hence option D is correct
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Joined: 23 Jul 2015
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Re: The City Opera House is expanding. Currently the city block containing  [#permalink]

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05 Mar 2017, 06:48
vikasp99 wrote:
The City Opera House is expanding. Currently the city block containing the opera house is rectangular-shaped with a total volume of 9600 feet. If the expanded Opera House is 2.5 times as long, wide, and deep as the original building, what would the new volume be?

A. 24,000
B. 60,000
C. 72,000
D. 150,000
E. 245,000

$$2.5l*2.5w*2.5h = (2.5)^3* l*w*h = (5/2)^3 * 9600 = 125/8 * 9600 =125* 1200 = 150000$$

Ans. D
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Posts: 2825
Re: The City Opera House is expanding. Currently the city block containing  [#permalink]

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07 Mar 2017, 17:29
vikasp99 wrote:
The City Opera House is expanding. Currently the city block containing the opera house is rectangular-shaped with a total volume of 9600 feet. If the expanded Opera House is 2.5 times as long, wide, and deep as the original building, what would the new volume be?

A. 24,000
B. 60,000
C. 72,000
D. 150,000
E. 245,000

Since volume = width x length x height, and the current volume of the opera house is 9,600, when the length, width, and height each becomes 2.5 times as large as the original, the new volume will be:

9,600 x 2.5 x 2.5 x 2.5 = 150,000 ft^3

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Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 192
Location: India
Re: The City Opera House is expanding. Currently the city block containing  [#permalink]

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30 Jul 2017, 20:59
So the new volume is 2.5(length)*2.5 (width)*2.5(depth)= 2.5(l*w*d)=2.5(9600)=24000
Can someone explain why is this method incorrect??
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Joined: 02 Sep 2009
Posts: 54376
Re: The City Opera House is expanding. Currently the city block containing  [#permalink]

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30 Jul 2017, 21:05
longhaul123 wrote:
So the new volume is 2.5(length)*2.5 (width)*2.5(depth)= 2.5(l*w*d)=2.5(9600)=24000
Can someone explain why is this method incorrect??

You have 2.5 thrice there! 2.5(length)*2.5 (width)*2.5(depth) = 2.5^3*(length)*(width)*(depth).

P.S. Every solution above explains this. Have you read them?
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Re: The City Opera House is expanding. Currently the city block containing   [#permalink] 30 Jul 2017, 21:05
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