A led pencil consists of a cylindner of wood with a solid cylinder of graphite filled into it. the diameter of pencil is 7mm, the diameter of graphite is 1 mm and the length of the pencil is 10cm. Calculate the weight of the whole pencil, if the specific gravity of the wood is `0.7 (gm)//(cm)^3` and that of graphite is `2.1 (gm)// (cm)^3`

Explanation

Given:
Diameter of the graphite cylinder`=1mm=1/10cm`
Radius`=1/20cm`
Length of the graphite cylinder`=10cm`
Volume of the graphite cylinder`=(22/7×1/20×1/20×10)cm^3`
Weight of graphite`=`Volume `×`Specific gravity
Weight of graphite`=(22/7×1/20​×1/20​×10×2.1)gm=gm=0.165gm`
Diameter of pencil `=7mm=7/10cm`
Radius of the pencil`=7/20cm` and length of pencil`=10cm`
Volume of pencil`=22/7×7/20×7/20×10cm^3`
Volume of wood`=(22/7×7/20×7/20xx10−22/7×1/20×1/20×10)cm^3`
Volume of wood`=22/7×1/20×1/20×10(7×7−1)cm^3=11/7×1/20×48cm^3`
Weight of wood`=(11/7×1/20×48×0.7)gm=2.64gm`
Total weight`=(2.64+0.165)gm=2.805gm`
Hence, the weight of the whole pencil is `2.805gm`.