F.3 數學 面積與體積?

The figure shows with dimensions a paper cup in the form of an inverted right circular cone and containing some water.

(a) Find the base radius of the water in the cup

(b) Find the extra volume of the water required to fill up the cup.

1 個解答

• SC147
Lv 6
4 年前
最愛解答

(a) △VRS ~ △VPQ (AAA)

∴ RS/PQ = VR/VP . . . . . . . . . (*)

=> RS/6 = 1.5/4.5

=> RS = 6(1/3) = 2 cm

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Note :

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(*) If 2 △s are similar, then their corresponding sides are proportional.

i.e. If △ABC ~ △XYZ, then AB/XY = BC/YZ = AC/XZ

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(b) capacity of cup . . . . . . . . . . . ]

= (1/3)πr²h . . . . . . . . . . . . . . . . . ] (#)

= (1/3)π(6²)(4.5)

= 54π cm³ . . . . . . . . . . . (i)

volume of water in cup

= (1/3)πr²h

= (1/3)π(2²)(1.5)

= 2π cm³ . . . . . . . . . . . . (ii)

∴ extra volume of water (to fill up the cup)

= 54π - 2π . . . . . . . . . . . . [from (i) - (ii)]

= 52π cm³

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Formula :-

(#) For a right circular cone with base radius r & height h,

volume = (1/3)πr²h