F.2-F.3Math (15marks)

用戶36732

2008-07-27 9:47 pm

We can estimate the volume of a sphere in the following ways.Method11. Measure the diameter of the sphere by a measuring tool and use the formula V=4/3pi r^3, where r is the radius, to find out its volume. If the diameter of the sphere is 10cm, corrected to the nearest 5 mm, finda) the maximum absolute error of the radius;b) the volume of the sphere;c) the maximum error of the volume of the sphere.(Hint:Maximum absolute error=Maximum value of volume-Estimate volume)Method22. As shown in the following figure, the volume of water displaced is the same as that of the sphere.跟住有幅圖, 就係話有杯水(唔知容量係幾多), 放左個sphere落水之後有520cm^3溢出If the volume of water displaced is 520cm^3, corrected to the nearest 10cm^3, find the maximum absolute error.詳細d, 比埋步驟我...thx!!!

回答 (1)

Ellen

2008-07-28 8:40 am

✔ 最佳答案

1.
a) the maximum absolute error of the radius
= 1/2(5mm) = 2.5mm = 0.25cm
b) the volume of the sphere:
= 4/3pi (5)^3 = 523.599cm^3
c)
the upper limit of the radius
= 5cm + 0.25cm = 5.25cm
the upper limit of the volume of the sphere
= 4/3pi (5.25)^3 = 606.131cm^3
the maximum error of the volume of the sphere
= 606.131cm^3 - 523.599cm^3
= 82.532cm^3
2.
the maximum absolute error
= 1/2(10cm^3) = 5cm^3

2008-08-01 10:40:44 補充：
maximum absolute error 只係計corrected to the nearest 值的一半,無乜步驟架喎,1a都係咁計,
只係按需要轉番個單位做cm

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