Answer to Question #178393 in Geometry for Raghav

Question

It was decided to put 20 street lights on a lonely road in order to secure the area at night. Each light was in the shape of a right circular cone mounted on a right circular cylinder having base radius 40 cm. Height of cylindrical part is 45 cm and that of conical part is 30 cm. Based on the above information in the statement of the question, find the surface area of a street light and if it costs `15 per 100 cm2? What will be the cost to install above mentioned lights?

Answer 1

Given;

Number of street lights (n) = 20

Base Radius of cylinder (r) = Radius of cone (r) = 40 cm

Height of cylinder (h) = 45 cm

Height of cone (h_c) = 30 cm

Cost of installation = '15 per 100cm²

Solution;

Let L be the slant height of the cone

Therefore, L = (h_c² + r²)^1/2 ...........1)

= (30² + 40²)^1/2

= (2500)^1/2

L = 50 cm

Now, lets find the the surface area (A)

• Right circular cylinder

A = 2$\pi rh ...........2)$

= 2 * $22/7$ * 40 * 45 = 11,309.73355 cm²

• Right circular con

A_C= $\pi rL ..............3)$

= 22/7 * 40 * 50 = 6,283.18531 cm²

• Total surface area (A_T)

A_T = n(A + A_C) ................4)

= 20(11,309.73355 + 6,283.18531) cm²

= 351,858.3772 cm²

Hence total cost of 20 street light is

= A_T * '15/100 ..............5)

= 351,858.3772 * 15/100

= '52,778.75658

Which is approximately '52800