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Question:

A rectangular swimming pool is 48 m long and 20 m wide. The shallow edge of the pool is 1 m deep. For every 2.6 m that one walks up the inclined base of the swimming pool, one gains an elevation of 1 m. What is the volume of water (in cubic meters), in the swimming pool? Assume that the pool is filled up to the brim.

Explanation:

Since the elevation increases by 1 m for every 2.6 m,

$x = \sqrt{2 . 6^{2} - 1} = \sqrt{6.76 - 1} = \sqrt{5.76} = 2.4 m$

Since $\frac{48}{2.4} = 20,$

The height of the deeper end of the pool is 20 m.

This can be represented as follows,

The total volume of water in the pool,

$(\frac{1}{2} \times 48 \times 20) \times 20 + (48 \times 20 \times 1)$

⇒ 48× 20 × 11

⇒ 10560 m³

Hence, option (d).

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