A pipe has a right prism shape with an equilateral triangle base of side 6 cm and length 40 cm. Find its water-holding capacity.
623.5 cm³
A right prism holds water equal to its volume, and the volume of a prism is the area of its uniform cross-section (the base) multiplied by its length.
The base is an equilateral triangle of side 6 cm, whose area \(= \frac{\sqrt{3}}{4}\times a^2 = \frac{\sqrt{3}}{4}\times 6^2\).
\(= \frac{\sqrt{3}}{4}\times 36 = 9\sqrt{3} \text{ cm}^2\).
Taking \(\sqrt{3}\approx 1.732\), base area \(= 9 \times 1.732 = 15.588 \text{ cm}^2\).
Volume \(= \text{base area}\times \text{length} = 15.588 \times 40 \approx 623.5 \text{ cm}^3\).
Key concept: volume of any right prism \(= \text{cross-sectional area}\times \text{length}\), with the equilateral-triangle area formula \(\frac{\sqrt{3}}{4}a^2\) for the base.
Hence the water-holding capacity of the pipe is 623.5 cm³.
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