Question

The cross-section of a perpendicular to its length is a trapezium ABCD as shown in the figure also given that :
AM = BN; AB = 7 m; CD = 5 m. The height of the tunnel is 2.4 m. The tunnel is 40 m long. Calculate the cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per $m^2$ (sq. metre.).

• A. Rs. $2040$
• B. Rs. $3040$
• C. Rs. $2140$
• D. Rs. $2240$

Answer 1

The correct option is A Rs. $2040$

$AM=BN=\frac{7-5}{2}$

=$\frac{2}{2}$

=$1m$

In $△ADM$
$A{D}^2=A{L}^2+D{L}^2$
$=>A{D}^2=1^2+{2.4}^2$
$=>A{D}^2=1+5.76$
$=>A{D}^2=\sqrt{6.76}$
$=>AD=2.6m$

Perimeter of the cross section of the tunnel =$(5+2.6+2.6+7)m$
=$17.2m$
Length =$40m$

$\therefore$ internal area of the tunnel(except floor)
=$17.2\times 40-40\times 7$
=$688-280$
=$408m^2$

Rate of painting=$5m^2$
=$408\times 5m^2$
=$2040$Rs