Question

# 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.

A

429.8 , No

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B

426.8 , Yes

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C

426.5 , No

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D

426.5 , Yes

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Solution

## The correct option is A 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.

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