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Ayla wishes to estimate the number of trees on a square block of land measuring 1000 m by 1000 m - HSC - SSCE Mathematics Standard - Question 17 - 2020 - Paper 1

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Ayla wishes to estimate the number of trees on a square block of land measuring 1000 m by 1000 m. She counts the number of trees on a 5 m by 5 m section of the block... show full transcript

Worked Solution & Example Answer:Ayla wishes to estimate the number of trees on a square block of land measuring 1000 m by 1000 m - HSC - SSCE Mathematics Standard - Question 17 - 2020 - Paper 1

Step 1

Count of Trees in the Sample Area

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Answer

Ayla counts 8 trees in the 5 m by 5 m section.

Step 2

Calculate the Area of the Sample Section

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Answer

The area of the 5 m by 5 m section is calculated as:

Area=5extmimes5extm=25extm2Area = 5 ext{ m} imes 5 ext{ m} = 25 ext{ m}^2

Step 3

Calculate the Total Area of the Block

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Answer

The total area of the square block of land is:

TotalextArea=1000extmimes1000extm=1,000,000extm2Total ext{ Area} = 1000 ext{ m} imes 1000 ext{ m} = 1{,}000{,}000 ext{ m}^2

Step 4

Proportional Calculation of Trees

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Answer

Using proportions to find the total number of trees (let x be the required number of trees):

825=x1,000,000\frac{8}{25} = \frac{x}{1{,}000{,}000}

Cross multiplying gives:

8×1,000,000=25x8 \times 1{,}000{,}000 = 25x

Thus,

x=8,000,00025=320,000x = \frac{8{,}000{,}000}{25} = 320{,}000

Step 5

Final Estimation of Trees on the Block

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Answer

Therefore, the estimated number of trees on the entire square block of land is 320,000 trees.

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