There are two tea shops in the friendly neighbourhood around our office. Shop 1 has been our only option for coffee/tea for the last few years. We discovered shop 2 over the last couple of weeks. The taste of tea in both shops is comparable. However, the shape of the tea glasses amused me enough to spend some cognitive space on a scientific analysis.
The shapes of the tea glasses used by both shops are represented in Figure 1.
Figure 1 – shapes of tea glasses in shops 1 and 2
Glass 1 is shaped like a cylinder, glass 2 is shaped like the frustum of a right circular cone. The heights of both glasses are same. This observation led me to make some calculations of basic geometry. Figure 2 shows the schematic diagrams of glass 1 and glass 2.
Figure 2 – schematic geometrical diagrams of glasses 1 and 2
Calculation of Volumes:
Glass 1 –
Height h = 7 cm
Radius r = 2.5 cm
|Volume of glass 1||=||Volume of cylinder|
|=||3.14 x (2.5)2 x 7 cm3|
Glass 2 –
Height h = 7 cm
Radius r1 = 2.5 cm
Radius r2 = 2 cm
|Volume of glass 2||=||Volume of frustum of cone|
|=||1/3πh (r12 + r22 + r1r2) cm3|
|=||1/3 x 3.14 x 7 ((2.5)2 + 22 + 2.5×2)) cm3|
Comparison of cost:
For the sake of calculation, let us equate the volume of the solid to the volume of the liquid it holds. Glass 1 holds 137 ml of tea and glass 2 holds 112 ml of tea. Shop 1 sells one glass of tea for 10 Rs, shop 2 sells one glass of tea for 7 Rs. Therefore shop 1 sells 13.7 ml of tea per rupee and shop 2 sells 16 ml of tea per rupee.
Mathematics tells us that drinking tea at shop 2 is more cost effective. The facts that shop 2 is just two doors down the road and delivers to our office form the icing on the cake.
Why go to all this trouble?
The decision to drink tea at one shop or the other is a matter of convenience and personal choice. Also, common sense can tell us which tea is more cost-effective. However, using basic Mathematics to arrive at this conclusion was a cognitive exercise that I thoroughly enjoyed.
Look around you. Find ways to use your subject knowledge to amuse yourself. Better still, encourage your children to do the same. The next time a child asks you, “where will I use all these mathematical formulae in my life?”, throw a similar problem for them to solve. When learning becomes amusing, you can’t draw the learner away from it.
We at NumberNagar® strive to connect concepts that children learn in schools to their everyday life. As facilitators, we take pleasure in practising what we preach. This is one part of my job that I love.
Featured image – Pixabay