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

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## Step 1: Given dataDensity of copper $=8.8\mathrm{g}/\mathrm{cc}$Weight in air $=264\mathrm{g}$Weight in water $=221\mathrm{g}$We have to find the volume of the cavity.Step 2: Finding the volume of copper block and the total volume of copper block + cavityMass of copper in air $=264\mathrm{gm}$Mass of copper in water $=221\mathrm{gm}$Apparent loss of mass in water $=264–221=43\mathrm{gm}$Mass of water displaced by copper piece when completely immersed in water$=43\mathrm{gm}$Volume of water displaced $=\frac{\mathrm{mass}\mathrm{of}\mathrm{water}\mathrm{displaced}}{\mathrm{density}\mathrm{of}\mathrm{water}}=\frac{43}{1}=43\mathrm{cc}$We know, the volume of water displaced = the volume of copper immersedTherefore, the volume of the copper piece including the volume of the cavity$=43cc$Volume of copper block excluding the cavity $=\frac{\mathrm{mass}\mathrm{of}\mathrm{copper}}{\mathrm{density}}=\frac{264}{8.8}=30\mathrm{cc}$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 $={\mathrm{V}}_{\mathrm{water}}-{\mathrm{V}}_{\mathrm{copper}}$$=43-30$$=13$Hence, the volume of the cavity is $13\mathrm{cc}$.  Suggest Corrections  2      Similar questions  Explore more