F3 Mensuration. be quick

👨🏻‍🏫 學術台數學

VINZ

2010-07-04 7:18 pm

1. When a metal rod is heated, the length of the rod increases by 8%. Find the percentage increase in volume of the metal rod.

更新1:

2. The ratio of the radius of metal ball A to that of metal ball B is 2:3. After melting the two metal balls, all the metal is used to recast metal ball C. (a) Find the ratio of the volume of the metal ball B to that of metal ball C.

更新2:

(b) If the volume of metal ball B is 441pi/10 (cm^3), find the radius of metal ball C.

回答 (1)

用戶10012

2010-07-04 7:55 pm

✔ 最佳答案

Since the shape of the metal rod is unchanged after heating, the shape before and after heating can be considered as similar figures.
Let volume before heating be V, length of rod before heating be x.
so length after heating = x(1 + 8%) = 1.08x
Volume after heating/V = (1.08x/x)^3 = 1.08^3 = 1.259712
So % increase in volume = (1.259712V - V)/V x 100% = 25.97%.

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