Question

A circular tunnel of diameter 2m and length 1.4km is dig out find the cost of plastering it at ₹150 per 100m square.

Answer 1

Diameter of circular tunnel = 2m
Radius of the circular tunnel = 1m
Height of the circular tunnel = 1.4 km
=1400 m

Area to be plastered = (2×22/7×1×1400)+(22/7×1×1)
=8800+22/7
=(61600+22)/7
=61622/7 m square

Cost of plastering 1 m Sq. = 150 per m Sq.
Cost of plastering 61622/7 m Sq. = 150×(61622/7)
=1320471.42 (approx.)

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

$\textbf{\underline{Shape\;of\;Circular\;tunnel=Cylinder}}$

Given:

D of tunnel = 2 m

${\boxed{\sf\:{radius=\dfrac{Diameter}{2}}}}$

${\boxed{\sf\:{r=\dfrac{2}{2}}}}$

r = 1m

${\boxed{\sf\:{H\;of\;Tunnel}}}$

= 1.4 km

$\textbf{\underline{Convert\;it\;into\;m}}$

= 1.4 × 1000

= 1400 m

${\boxed{\sf\:{CSA\;of\;Cylinder=2\pi rh}}}$

$\tt{\rightarrow 2\times\dfrac{22}{7}\times 1\times 1400}$

2 × 22 × 200 = 44 × 200

= 8800 m²

$\textbf{\underline{Cost\;of\;Plastering}}$

= CSA of Cylinder × Rate

$\tt{\rightarrow\dfrac{8800\times 150}{100}}$

= 88 × 150

= ₹ 13200

Therefore,

${\boxed{\sf\:{Cost\;of\; Plastering\;is 13200}}}$