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Question

A piece of copper having an internal cavity weighs 264g in air and 221g in water, Find the volume of the cavity. (Take the density of copper as 8.8g/cc).


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Solution

Step 1: Given data

Density of copper =8.8g/cc

Weight in air =264g

Weight in water =221g

We have to find the volume of the cavity.

Step 2: Finding the volume of copper block and the total volume of copper block + cavity

Mass of copper in air =264gm

Mass of copper in water =221gm

Apparent loss of mass in water =264221=43gm

Mass of water displaced by copper piece when completely immersed in water=43gm

Volume of water displaced =massofwaterdisplaceddensityofwater=431=43cc

We know,

the volume of water displaced = the volume of copper immersed

Therefore, the volume of the copper piece including the volume of the cavity=43cc

Volume of copper block excluding the cavity =massofcopperdensity=2648.8=30cc

Step 3: Find the volume of the cavity.

The volume of the piece of copper including the cavity is equal to the volume of water.

Therefore,

Volume of cavity =Vwater-Vcopper

=43-30

=13

Hence, the volume of the cavity is 13cc.


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