Below is a photograph of an island. The highest point on the island is 916 metres above sea level. Using this information, and the photograph, estimate as accurately as possible the volume of the island that is above sea level. Give your answer in the form $a \times 10^n$, where $n \in \mathbb{Z}$ and $1 < a < 10$. State clearly any assumptions that you make in finding your answer.

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Below is a photograph of an island - Junior Cycle Mathematics - Question 1 - 2015

Question 1

Below is a photograph of an island. The highest point on the island is 916 metres above sea level. Using this information, and the photograph, estimate as accurately... show full transcript

Worked Solution & Example Answer:Below is a photograph of an island - Junior Cycle Mathematics - Question 1 - 2015

Step 1

Measuring from the top of the island to sea-level

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Answer

The height of the island in the picture is approximately 4.5 cm. This measurement may vary depending on your printer, but we will use this estimate. To find the actual height corresponding to 916 m, we note that 1 cm in the picture corresponds to about 203.56 m.

Step 2

Estimating the width of the island

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Answer

The width of the island at sea level is approximately 12 cm, which translates to about 12 * 203.56 = 2442.72 m.

Step 3

Calculating the radius of the cone

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Answer

Assuming the island has a conical shape, the radius (half of the diameter) is 1212.36 m.

Step 4

Calculating the volume of the island

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Answer

The volume $V$ of the cone can be calculated using the formula $V = \frac{1}{3} \pi r^2 h$ Substituting the values, we have: $V = \frac{1}{3} \pi (1212.36)^2 (916) \approx 1.430907225 \times 10^9 \text{ m}^3$

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