? day is upon us. The 14th of March represented as 3.14 is called ? day. (I would have preferred the 22nd of July). It is a mostly forgotten day because E-commerce has not yet co-opted it. But, we at 2IIM are definitely fascinated by it.
? has enamoured us for 4000 years
The ratio of circumference to diameter has intrigued mathematicians for millennia. The Babylonians were among the first to think about it – they came up to 3.125; Archimedes went further with the idea of inscribing and circumscribing a circle with regular polygons. Newton had a go at it, and our own Ramanujan gave some efficient ways of finding approximations.
The latest approximation (it is still an approximation) goes up to 50000000000000 digits. That is 5 followed by 13 zeroes and beauty lies in the idea that we could be at this game for a while yet.
4 interesting geometry questions to keep you engaged
We have picked up 4 excellent questions from different topics all related to ? to keep you engrossed. These are tougher than what you can expect in the CAT but are fun to try nevertheless. Send us your solutions by 3:00 PM, 14th March 2021 to info@2iim.com and we will feature the best ones on our blog. Here are the interesting geometry questions:
- Two square tiles of same size are stacked upon each other such that their centres coincide, but the top tile does not completely cover the bottom tile. If the length of the sides of the tiles is 1 unit. Show that the area that is common between the two tiles is always greater than 3/4.
- Two semicircles are placed in a circle as shown in the figure below. Find the area of the shaded region w.r.t the area of the circle.
3. Two semi circles and a circle are arranged in a rectangle as shown in the figure below. If the length of the rectangle is 10 units, find the area of the shaded region.
4. Pythagoras wanted to celebrate Pi day by sharing Pie with 100 of his friends. He serves 1% of the Pie to the first guest. 2% of the remaining Pie to the second guest. And 3% of the remaining to the third guest and so on… Which guest gets the largest share of the Pie?
To remind once again, please send across the answers to info@2iim.com before 3.00pm on 14th of March 2021 to get featured on our blog.
For more CAT questions from Geometry, head onto – 2IIM’s CAT Questionbank . Happy solving!
Detailed explanations with video solutions for the above tested questions will be made available soon. Watch out for this space.
Hakuna Matata
No discussion on ? ends without a reference to the Circle of Life and a call-out to the utterly delightful phrase ‘Hakuna Matata’. Hakuna Matata means ‘No worries for the rest of your Days’. We at 2IIM wish that you jump into this CAT journey, have plenty of fun preparing for it and subscribe to the carefree philosophy Hakuna Matata.
Happy CAT preparation to you all!
Rajesh Balasubramanian takes the CAT every year and is a 4-time CAT 100 percentiler. He likes few things more than teaching Math and insists to this day that he is a better teacher than exam-taker.
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