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Question

The volume of a spherical balloon with radius 4.1 cm is about 289 cm cubed. Estimate the volume of a similar balloon with radius 8.2 cm.

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Answer 1 · 2018-03-14T14:28:18

Volume of a similar balloon with radius #8.2cm# is about #2312cm^3#.

As #8.2/4.1=2#, ratio of volumes is #2^3:1^3=8:1#

Hence volume of a similar balloon with radius 8.2 cm is about#289xx8=2312cm^3#

Details Volume of first cylinder is #4/3pi(4.1)^3#

Volume of second cylinder is #4/3pi(8.2)^3#

Hence, ratio of volume of second ballon to that of first is #(4/3pi(8.2)^3)/(4/3pi(4.1)^3)=2^3=8#.

For more details in a similar case, please see here.