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

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vikasp99
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The City Opera House is expanding. Currently the city block containing [#permalink] New post   02 Mar 2017, 21:16
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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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D
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Re: The City Opera House is expanding. Currently the city block containing [#permalink] New post   02 Mar 2017, 22:43
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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.

Answer (D)
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Re: The City Opera House is expanding. Currently the city block containing [#permalink] New post   03 Mar 2017, 00:23
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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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Re: The City Opera House is expanding. Currently the city block containing [#permalink] New post   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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Re: The City Opera House is expanding. Currently the city block containing [#permalink] New post   07 Mar 2017, 17:29
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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

Answer: D
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Re: The City Opera House is expanding. Currently the city block containing [#permalink] New post   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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Re: The City Opera House is expanding. Currently the city block containing [#permalink] New post   30 Jul 2017, 21:05
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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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