Answer to Question #120220 in Physics for Tapajyoti Banik

Question

One suggestion to reduce the usage of fossil fuels is to cover all the roofs in India with solar
collectors.
(a) What simple geometric shape can you use to approximate the shape of India?
(b) Using reasonable guesses and using your shape above, find the area of India in square
kilometers.
(c) Convert it to square meters.
(d) Guess what percentage of that area is occupied by buildings with roofs?
(e) A typical solar panel produces about 200 watts of electricity per square meter. Using this
find the power generated by the solar collectors in gigawatts. Compare it with the power
generated by coal in India which is 200 GW.

Answer 1

(a) What simple geometric shape can you use to approximate the shape of India? According to the (https://en.wikipedia.org/wiki/India#/media/File:India_(orthographic_projection).svg), the shape should be the rhombus:

(b) Using reasonable guesses and using your shape above, find the area of India in square

kilometers. 

Let the vertical diagonal of the rhombus be $d_1 = 3\cdot 10^6km$ and the horizontal diagonal be $d_2 = 2.3 \cdot 10^6 km$ (which is reasonable according to the map scale). Then the area of India will be:

$$A = \dfrac{d_1d_2}{2} = 3.45 \cdot 10^6 km^2$$

(c) Convert it to square meters:

$$A = 3.45 \cdot 10^6 km^2 = 3.45 \cdot 10^{12} m^2$$

(d) Guess what percentage of that area is occupied by buildings with roofs? 

The population of India is $1.3\cdot10^9$ people. Let each 100-th has the building with roof (taking into account thouse who lives in cities). Thus, we have $2.6\cdot 10^7$. Suppose, each roof has the area $110 m^2$. Thus, the total roof area will be $2.8\cdot 10^9 m^2$. The percentage of total area occupied by buildings with roofs will be:

$$P = 2.8\cdot 10^9m^2/A\cdot 100\% = \dfrac{2.8\cdot 10^9m^2}{3.45 \cdot 10^{12}}100\% = 0.08\%$$

(e) A typical solar panel produces about 200 watts of electricity per square meter. Using this

find the power generated by the solar collectors in gigawatts. Compare it with the power

generated by coal in India which is 200 GW.

The power generated by the solar collectors will be:

$$E = 200\cdot2.8\cdot 10^9 m^2 =560 GW$$

This is more then 2 time greater then the power generated by coal in India.