Question

The tent for an exhibition is as shown below, with a half-cylinder on top of a rectangular prism.

What is the cost of making it, at the rate of 2000 rupees per square metre.

Answer 1

Length of the rectangular prism = 18 m

Breadth of the rectangular prism = 3 m

Diametre of the cylinder = Breadth of the rectangular prism = 3 m

∴ Radius (r) of the cylinder =

Height (h) of the cylinder = 18 m

Height of the rectangular prism = Total height − Radius of the cylinder

= (6 − 1.5) m

= 4.5 m

Lateral surface area of the rectangular prism = Base perimeter × Height

= 2 (Length + Breadth) × Height

= 2(18 + 3) × 4.5 m²

= (42 × 4.5) m²

= 189 m²

Lateral surface of the half cylinder = × Base perimeter × Height

= × 2πr × h

= (3.14 × 1.5 × 18) m²

= 84.78 m²

Area of two semicircles at the ends of the cylinder = 2 ×× π × r²

= (3.14 × 1.5 × 1.5) m²

= 7.065 m²

Total area of the tent = Lateral surface area of the rectangular prism + Lateral surface of the half cylinder + Area of two semicircles at the ends of the cylinder

= (189 + 84.78 + 7.065) m²

= 280.845 m²

Cost of making the tent per sq. metre = Rs.2000

∴ Cost of making the tent of area 280.845 m² = Rs.2000 × 280.845 = Rs.561690