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中三數學 - area and volume
The surface area of a spherical balloon is first increased by 125% and then decreased by 19%. Find the overall percentage change in
(a) radius (b) its volume.
請高人指點. thanks !
1 個解答
- ?Lv 71 十年前最愛解答
First, we need to compute the final percentage increase of the surface area.
Let the original surface area be y.
The new surface area
= y( 1 + 125% ) ( 1 - 19% )
= y( 2.25 )( 0.81 )
= 1.8225y
The surface area is increased by 82.25%
From the similar solid concepts, we realize that if the ratio of the surface area is 1 : y, then for radius the ratio is 1 : Root ( y ) and the volume is 1 : ( y )^3/2.
Since Root ( 1.8225 ) = 1.35
Hence, the percentage change of radius is + 35%
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Similarly, ( 1.8225 )^3/2 = 2.460375 = 2 + 146.0375%
Hence, the percentage change of Volume is + 146.0375%
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Hope I can help you.
資料來源： Mathematics Teacher Mr. Ip
