中三數學 - area and volume

雅各

2011-03-06 4:45 am

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 !

回答 (1)

良師益友

2011-03-06 6:14 am

✔ 最佳答案

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.

參考: Mathematics Teacher Mr. Ip

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