F.3 數學 面積與體積?

(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