A geographer is constructing a statistical map using proportional circles to represent agr… — JAMB UTME

A geographer is constructing a statistical map using proportional circles to represent agricultural output across regions. Region A produced $100{}000\text{ metric tonnes}$ of cassava and is drawn with a circle radius of $1.5\text{ cm}$ . If Region B produced $400{}000\text{ metric tonnes}$ of cassava, what is the correct radius required for the circle representing Region B?

$3.0\text{ cm}$ Answer
B
$6.0\text{ cm}$
C
$0.75\text{ cm}$
D
$4.5\text{ cm}$

Answer

The radius required for the circle representing Region B is

3.0\text{ cm}

For proportional circle maps, the visual area of each symbol must be directly proportional to the magnitude of the data represented (

A \propto V

). Since the area of a circle is

A = \pi r^2

, the radius

r

is proportional to the square root of the statistical value (

r \propto \sqrt{V}

). The output ratio between Region B and Region A is

400{}000 / 100{}000 = 4

. The square root of this ratio gives a radius scale factor of

\sqrt{4} = 2

. Multiplying Region A's circle radius of

1.5\text{ cm}

2

gives

3.0\text{ cm}

Step-by-Step Solution

Calculate the ratio of the quantities represented by the two regions

Data Value Ratio =

\frac{400{}000}{100{}000} = 4

Determining how many times larger Region B's output is compared to Region A.

Apply the proportional symbol area scaling formula (

r \propto \sqrt{V}

)

Radius Scale Factor =

\sqrt{4} = 2

Because a circle's area is proportional to the statistical value (

A \propto V

), the radius must scale with the square root of the value ratio.

Calculate the required radius for Region B

Radius =

1.5\text{ cm} \times 2 = 3.0\text{ cm}

Multiplying the base radius of Region A by the radius scale factor.

Key Concept

Proportional Symbol Map Scaling (Square Root Radius Rule)

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