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01 Aug 2023, 03:00
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D
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Difficulty:
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75% (02:25) correct
25%
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wrong
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A spherical balloon originally had a radius of x centimeters. The balloon was partially deflated by letting out some air so that the volume of the balloon decreased by a%. If the balloon remained spherical while the air was being let out, which of the following expressions in x and a gives the radius, in centimeters, of the partially deflated balloon?
(Note: The volume of a sphere with radius r is \(\frac{4}{3}πr^3\).)
A. \(x(100 - a)^3\)
B. \(x(1 - \frac{a}{100})^3\)
C. \(x(\sqrt[3]{100 - a})\)
D. \(x(\sqrt[3]{1 - \frac{a}{100}})\)
E. \(x(1 - \sqrt[3]{\frac{a}{100}})\)
(Note: The volume of a sphere with radius r is \(\frac{4}{3}πr^3\).)
A. \(x(100 - a)^3\)
B. \(x(1 - \frac{a}{100})^3\)
C. \(x(\sqrt[3]{100 - a})\)
D. \(x(\sqrt[3]{1 - \frac{a}{100}})\)
E. \(x(1 - \sqrt[3]{\frac{a}{100}})\)
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01 Aug 2023, 07:27
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Bunuel
The original volume of the balloon is:
(4/3)(pi)(x^3)
Since an a% decrease corresponds to a factor of (1 - a/100), the volume of partially deflated balloon is:
(4/3)(pi)(x^3)(1 - a/100)
If r is the radius of the partially deflated balloon, we have:
(4/3)(pi)(r^3) = (4/3)(pi)(x^3)(1 - a/100)
r^3 = (x^3)(1 - a/100)
r = (x)(root[3](1 -a/100))
Answer: D
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lg800
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14 Oct 2023, 13:42
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Any suggestions on ways to do this by plugging in?
