A Ramraj pencil box of dimensions 30cm × 5cm × 5cm consists of 10 sharpened cylindrical pencils placed in a vertical fashion each of length 20cm and diameter 1.4cm and having a conical surmount whose slant height is 2.5m. There are 2 rows of 5 pencils each. Find available volume in the box. Can a sharpener and an eraser in shape of a cube each of side 5cm be placed on top of the pencils such that sharpener is placed on top of the eraser.
429.8 , No
Lets compute the volume of a sharpened pencil.
Volume of 1 pencil = volume of the cylindrical part + volume of the conical part
= πr2H+13πr2h
h2=(2.5)2−(0.7)2=5.76
⇒ h=2.4
= 3.14×0.72[20+2.43]
= 32.02 cm3
Volume of 10 pencils =320.2 cm3
Volume of the pencil box = 30×5×5 = 750 cm3
Available volume = 750 – 320.2 = 429.8 cm3
Analysing the volume, the answer should be a yes, but considering the dimensions of the box we cannot have both an eraser and a sharpener.
Length of the box=30cm.
Length of the sharpened pencil = 20 + 2.4 = 22.4
Length of the eraser and sharpener = 10cm
Since length of the sharpener +eraser+pencil > length of box , it is not possible.