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IBDP Mathematics Question Analysis - Mathematics - Volume

IBDP Mathematics Question Analysis

· IBDP Mathematics,ib mathematics,volume surface area,Volumes

IBDP Mathematics Question Analysis Topic: Mathematics - Volume

Exam Question:

A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.

Answer:

For IBDP Mathematics, you should know:

Given: diameter = 36cm, radius = 18cm

So, the volume of the hemispherical bowl is:
2/3πr3 = 2/3 x 22/7 x (18)3 = 12219.43cm3

Also given: radius of cylinder = 3cm

Volume of 72 bottles = 22/7 x (3)2 x h x 72

10% of 12219.943 --> 1221.943cm3 of liquid is wasted, making the remaining volume 10997.487cm3

Therefore:
72 x 22/7 x 3 x 3 x h = 10997.487cm3

--> h = 10997.487 x 7 / (72 x 22 x 9) = 5.4cm, where h is the height of each bottle.

Work hard for your IBDP Mathematics examination!

End of analysis. Great!

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