March 2015

# That's not a fair share!

It helps to know mensuration; I learned this (not mensuration, but the knowledge that it helps to know mensuration!) the hard way.

Well, it happened this way. It was a hot summer afternoon. The school had broken for summer vacations. My parents were away at work and I was all alone at home. I invited my friend, Shomu, to come over so that we could play some indoor game.

Shomu, let me tell you, is a math wizard. In the midst of our game, I felt thirsty. Mother had kept some soft drink for me in a metal container in the shape of a right circular cone. She had kept a single glass outside while locking up every other item of her precious crockery in the cabinet knowing my penchant for breaking them.

I don't know how this conical container came about in the house, but there it was. It was a right circular cone of height 12 cm (I had measured it). With a broad circular mouth and tapering off to a point at the bottom, it looked quite cute. Now, you must be wondering how the vessel could remain upright. Well, it had a stem and a stand like a wine glass.

I brought the container, filled to the brim with soft drink, and the only available glass. Now, how was I to pour out the soft drink into the glass in two equal portions?

"What is the problem?" Shomu asked with a twinkle in his eyes. "I don't much like soft drinks, so just pour four centimetres from the top into the glass and give it to me. You can have the larger share," Shomu said. This came as a surprise because I knew Shomu enjoyed soft drinks. An equal share would have meant pouring out six centimetres into the glass from the right conical vessel of height 12 centimetres (isn't that so?). Perhaps Shomu was acting the gentleman since he was my guest, I thought. Anyway, I was quite happy because I would be getting a larger share. So, I immediately took out the ruler from my geometry box and measured out 4 cm from the top and poured it into the glass. The height of the soft drink in the conical vessel now stood at 8 cm.

Strange! I finished my soft drink in a jiffy but Shomu was still sipping from the glass! He was enjoying the soft drink by sipping slowly from the glass, I thought. Or, was it that he had received a larger share of the soft drink? But how could that be? He had taken only 4 cms from the top while I had 8 cms. There was something amiss, I reckoned. Did I really get a larger share? Or, did Shomu pull a fast one on me?

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in