
A part chart is drawn to show the areas in millions of square km of several continents. The area of 11.7 square km of Africa is shown by a sector subtending an angle of \[{81^ \circ }\].If the subtended angle corresponding to North America is \[{63^ \circ }\],its area is:-
Answer
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Hint:Here in this question we will use the concept of unitary method. Unitary method is a technique in which we first find out the value of a single unit and then multiplying that unit to find necessary value.
Complete step-by-step answer:
In this we will first find out square km area of \[{1^ \circ }\] then by unitary method we will find out square km area of \[{63^ \circ }\]
$ \Rightarrow {81^ \circ }$ Angle subtended corresponding to area = 11.7 square km
$ \Rightarrow {1^ \circ }$ Angle subtended corresponding to area= $\dfrac{{11.7 \times {1^ \circ }}}{{{{81}^ \circ }}}$ square km
= $\dfrac{{11.7 \times {1^ \circ }}}{{{{81}^ \circ }}} = 0.145$ square km
$ \Rightarrow {63^ \circ }$ Angle subtended corresponding to area= $\dfrac{{{{63}^ \circ } \times 0.145}}{{{1^ \circ }}}$ square km
= $\dfrac{{{{63}^ \circ } \times 0.145}}{{{1^ \circ }}} = 9.135$ square km
Therefore if the subtended angle corresponding to North America is \[{63^ \circ }\], its area will be 9.135 square km.
Additional Information:Unitary method has two types of variations: -
1) Direct variation: - In this type of variation an increase or decrease in one quantity will cause an increase or decrease of another quantity. For example – Increase in the number of goods causes an increase in price of goods so they are directly related to each other.
2) Indirect variation: - In this type of variation an increase or decrease in one quantity will cause a decrease or increase of another quantity. For example - Increase in speed can cause decrease in the total distance which has to be covered.
Note:-Students may likely make mistakes by unnecessarily thinking of finding area through angle which is a very wrong approach to proceed. The method explained above is very effective and easy to implement.
Complete step-by-step answer:
In this we will first find out square km area of \[{1^ \circ }\] then by unitary method we will find out square km area of \[{63^ \circ }\]
$ \Rightarrow {81^ \circ }$ Angle subtended corresponding to area = 11.7 square km
$ \Rightarrow {1^ \circ }$ Angle subtended corresponding to area= $\dfrac{{11.7 \times {1^ \circ }}}{{{{81}^ \circ }}}$ square km
= $\dfrac{{11.7 \times {1^ \circ }}}{{{{81}^ \circ }}} = 0.145$ square km
$ \Rightarrow {63^ \circ }$ Angle subtended corresponding to area= $\dfrac{{{{63}^ \circ } \times 0.145}}{{{1^ \circ }}}$ square km
= $\dfrac{{{{63}^ \circ } \times 0.145}}{{{1^ \circ }}} = 9.135$ square km
Therefore if the subtended angle corresponding to North America is \[{63^ \circ }\], its area will be 9.135 square km.
Additional Information:Unitary method has two types of variations: -
1) Direct variation: - In this type of variation an increase or decrease in one quantity will cause an increase or decrease of another quantity. For example – Increase in the number of goods causes an increase in price of goods so they are directly related to each other.
2) Indirect variation: - In this type of variation an increase or decrease in one quantity will cause a decrease or increase of another quantity. For example - Increase in speed can cause decrease in the total distance which has to be covered.
Note:-Students may likely make mistakes by unnecessarily thinking of finding area through angle which is a very wrong approach to proceed. The method explained above is very effective and easy to implement.
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