News on the TV
India has made major improvements in grain production. However, the storage of grain is a problem. The twelve year old Tanya was watching the TV and saw this news item, “In Bihar, the people die of hunger not because not enough grain can be produced in the farms but because there is a shortage of storage and transport facilities of the grain. Bihar can produce up to 2.4 million tons of grain but it can store only about 25% of it properly. The government will spend Rs 1367 crore (Rs. 13670 million) for the year 2012-13 to improve storage of food grains, organic farming, green fertilizer and horticulture.”
These were all big numbers. Tanya talked to her Math teacher because he liked to explain things. The teacher says that he wanted to talk to the whole class about it the next day.
From bread to weight and volume of grain
Teacher: I am sure all of you ate roti yesterday. Do you know that one can make 40 rotis from 1 kilogram (kg) of wheat flour. A ton of flour is 1000 kg. That means you can make 40,000 rotis from one 1 ton of wheat.
Tanya: That is a lot of rotis. That means if every year Bihar can grow up to 2.4 million tons of wheat, that is enough for 40,000 x 2.4 million which is 96 billion rotis every year but the TV said that there was a storage problem.
Teacher: Wheat grains are typically stored as 50 kg per sack which is about 20 cm x 35 cm x 100 cm. They don’t have sharp corners but when filled with wheat they are about 20 x 35 x 100 cubic centimeters or you could say 0.20 x 0.35 x 1 cubic meters. That equals 0.07 cubic meters. The sacs can be stacked in large warehouses.
Kate: My uncle owns one. It is big, very big. I walked around it and it took me a long time.
Peter: Is it bigger than our school?
Storage warehouses
Kate: No but it is bigger than our class room. He told me that the warehouse was 100 meters long, 20 meters wide and 5 meters high.
Tanya: That means its floor area is 100 x 20 which is 2000 square meters. Being 5 meters high, it has a volume of 10,000 cubic meters. Wow, that is big.
Teacher: Because one sack of grain is only 0.07 cubic meters, the number of sacks it can contain is 10,000 divided by 0.07 which is 142857 or let us say more than 140,000 sacks. Because each sack has 50 kg grain, it can store 7,000,000 kg of grains which is 7000 tons.
Tanya: Now, I realize how big the problem is and why the government is spending so much money. This large warehouse can store only 7000 tons and Bihar needs to store 2.4 million tons of grain every year.
Silobags
Teacher: There are better solutions. Some states have started using Silobags. Each silobag is about 60 meters long, and 3 meters in diameter. It can store around 200 tons of grain. The bag is made from very thin three-layer plastic sheet. It protects the grain from rain, ultraviolet rays and other atmospheric conditions. Many Silobags can be placed on the fields when they are not being used by the farmers. Bihar needs to explore this possibility.
Tanya; Thank you Sir. I did not know about the Silobags. I think it is a good thing that the government is spending all this money to explore the grain storage problems. I wonder, if this money is enough.
Challenge
“Happy birthday” said papa to you and gave you a nice looking backpack. He told you that the backpack is very sturdy and weighs only 500 grams. You have books which are 25 cm long and 18 cm wide. Each book has about 200 pages which stack up to a height of 1 cm. You find that if you stack the books properly, you can put 6 books in it. Before, you get so happy, what is the volume of the books you can pack? If the paper has a density of 0.75 grams/cubic centimeters, how much total weight will you be lugging including the weight of the bag. This isn’t so bad, is it?
Solution: Each book is 25 cm long and 18 cm wide and 1 cm high. When stacked on top of each other, their volume becomes 25 x 18 x 6 cubic centimeters = 5400 cubic centimeters. The weight of the books will be 5400 cubic centimeters x 0.75 grams/cubic centimeters = 4050 grams. Adding the weight of the bag, the backpack will weigh 4050 + 500 grams or 4.55 kilograms.
Happy lugging. This isn’t so bad, is it?
Math Stories For You 