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Re: The radius of a sphere was increased by p percent. If the volume of th
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07 Feb 2022, 09:04
Remember. An increase is a positive change between a final amount and an initial amount.
An increase of 20% is:
Final amount - Initial amount = 20% of the initial amount
Final amount - initial amount = (20/100) x (Initial amount)
Thus, if the volume of a sphere was increased by 33.1%, then:
Final Volume - Initial Volume = 33.1% of Initial Volume
This is:
Final volume - initial volume = (33.1/100) x (initial volume)
Final volume = initial volume + (33.1/100) x (initial volume)
Final volume = (100/100) x (initial volume) + (33.1/100) x (initial volume)
Final volume = (133.1/100) x (initial volume)
4/3Pi(R)exp3 = (133.1/100) x 4/3 Pi(r)exp3
Then (R)exp3 = (133.1/100)x(r)exp3
Applying cube root to both sides, we have:
R = (133.1/100)exp(1/3) x r
R = (1331/1000) exp(1/3) x r
R = (11/10) x r
R - r = (11/10) xr -r
R -r = (11/10)xr - (10/10)xr
R-r = (1/10)xr
R-r = (10/100)xr
Then the radius increased by 10%
Answer B