Question

Allocations to various sectors of the yearly budget for Rs $1000$ crore are represented by the following pie diagram. The expenditure (in rupees) on agriculture.

Industry$={{18}^{0}}$, Education$={{90}^{0}}$, Defence$={{72}^{0}}$, Technology$={{54}^{0}}$ , Misc$={{54}^{0}}$
$A.250$ Crore
$B.150$ Crore
$C.300$ Crore
$D.200$ Crore

Answer 1

Hint: Here the pie diagram shows the angle of each sector. We know that the angle of the circle is ${{360}^{0}}$ Adding all the angles and equals to ${{360}^{0}}$. We get the agriculture value in angle. Then convert angle in rupees by dividing the angle of agriculture by angle of circle then multiply the yearly budget we get the expenditure on agriculture.

Complete step-by-step answer:
Here the angle of full circle is ${{360}^{0}}$
Given that Industry$={{18}^{0}}$, Education$={{90}^{0}}$, Defence$={{72}^{0}}$, Technology$={{54}^{0}}$ , Misc$={{54}^{0}}$
And we need to find angle of agriculture,
Adding all sectors of angle and equals the angle of full circle,
Take angle of agriculture as $x$
Then adding the angles we get,
$\Rightarrow {{18}^{0}}+{{90}^{0}}+{{72}^{0}}+{{54}^{0}}+{{54}^{0}}+x={{360}^{0}}$
Sum up all the values we get,
$\Rightarrow {{288}^{0}}+x={{360}^{0}}$
Further we get,
$\Rightarrow x={{360}^{0}}-{{288}^{0}}$
$\Rightarrow x={{72}^{0}}$
We get the angle of agriculture as ${{72}^{0}}$
Then we have yearly budget of Rs.1000 crore
We have to convert angle into expenditure for that we have,
Expenditure of agriculture = (angle of agriculture ÷ angle of full circle) × yearly budget
$\Rightarrow $ Expenditure of agriculture $=\dfrac{{{72}^{0}}}{{{360}^{0}}}\times 1000$
Simplify this we get,
$\Rightarrow $ Expenditure of agriculture $=200$ crore

Note: An angle of a circle is an angle which is formed between the radii, chords or tangents of a circle. Using that we can find the angle of others which are not given.