A divided bar chart of total length 15\text{ cm} is constructed to illustrate the land use… — JAMB UTME

A divided bar chart of total length $15\text{ cm}$ is constructed to illustrate the land use distribution of an agricultural zone covering a total area of $120,000\text{ hectares}$ . If livestock grazing occupies $32,000\text{ hectares}$ of this land, what is the length in $\text{cm}$ of the bar segment representing livestock grazing?

Answer: 4 cm

Answer

The length of the bar segment representing livestock grazing is

4\text{ cm}

The correct answer of

4\text{ cm}

is obtained by finding the fraction of total land devoted to grazing (

\frac{32,000}{120,000} = \frac{4}{15}

) and scaling it by the total bar length of

15\text{ cm}

Step-by-Step Solution

Calculate the proportion of the land area used for livestock grazing

Proportion =

\frac{32,000}{120,000} = \frac{4}{15} \approx 0.2667

Divided bar charts represent component parts proportionally relative to the whole dataset.

Multiply the proportion by the total bar length to find the length of the segment

Segment length =

\frac{4}{15} \times 15\text{ cm} = 4\text{ cm}

The total length of the bar represents

100\%

of the total area, so each sub-component's length is proportional to its contribution.

Key Concept

Calculating component segment lengths for divided bar charts using proportional ratios

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