4題 中2 數學題

1.
pay the money to buy 5 of each type of fruit
= 5 * ( 2 + 1.5 )
= $17.5
money left
= 65 - 17.5
= $47.5
the maximum no. of fruits he can buy
= 47.5/1.5 + 10 [because orange is the cheapest]
= 31...1 + 10
= 41

2.
Let the radius be r cm.
2 π r * 1/4 = 32 - 2r
π r = 64 - 4r
π r + 4r = 64
r ( π + 4 ) = 64
r = 64 / ( π + 4 )
the area eclosed by wire
= π r ^2 * 1/4
= π [64 / ( π + 4 )] ^2 * 1/4
= 1024π / ( π + 4 ) ^ 2 [using calculator]
= 63 cm^2 (cor. to the nearest cm^2)

由於你最少要每樣買5個，5(1.5+2)是必須買的....先買了十個水果
你還剩$65-5(1.5+2)=$47.5
買橙較平....剩下的全部買橙會買到較多...
47.5能買到......47.5/1.5=31.6666666667.........即係可以買到三十一個......
總數有四十一個

該條圓弧長32-2r cm
換一個計法圓弧長 1/4 (2πr)=1/2 (πr)
32-2r=1/2 (πr)
64-4r=πr
64=r(π+4)
r= 64/(π+4)
aera= 1/4 π (r ^2)
= 1/4 π [64/(π+4)]^2
= 1024π/ [(π+4)]^2 cm^2