A site has a unidirectional slope of 30° with horizontal

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A site has a unidirectional slope of 30° with horizontal along its longer side. The projected dimensions of the site on the horizontal plane measures 30 m × 40 m. Using cut and fill method the site has to be levelled parallel to the horizontal plane. The minimum amount of earth to be excavated in cubic metre is ____________

1. 463 to 546
2. 3463 to 3465
3. 3433 to 3665
4. 3461

Correct Option: B

Draw cross-section of site as shown in figure below.
Volume of existing site section = (Cross section Area) × Length of shorter side

=		1	× 40 × (tan 30° × 40)		× 30 = 13856 m³ ......(1)
		2

This volume needs to be converted into cuboid of dimensions 30m × 40m × h ...(2)
Equation 1 & 2
h = 11.546m (BF)
CF = BC – BF = (tan 30° × 40) – 11.546 = 11.548
As per 30 – 60 – 90 principle, EF = CF × √3 = 11.548 × √3 = 20 m
Thus, volume of area need to be cut and filled

=	1	× 20 × 11.546 × 30 = 3463 m³
	2