Acylinderical chemical drum is 220.5 cm long and the radius of the drum is 42 cm. calculate the cost of painting the drum akt the rate of rs. 0.15/cm

The surface area of the cylindrical drum of radius 21cm, height 50cm open at the top.

radius R = 42 cm

length L = 220.5 cm

bottom surface SB = 3.14 x R x R = 3.14 x 42 x 42 = 5539 square cm

top surface ST = 3.14 x R x R = 3.14 x 42 x 42 = 5539 square cm

bottom circumference BS = 3.14 x 2 x R = 3.14 x 2 x 42 = 264 cm

wall surface area WS = BS x L = 264 x 220.5 = 58212 square cm

whole outside surface area SB + ST + WS = 5539 + 5539 + 58212 = 69290 square cm

whole inside and outside surface area 69290 + 69290 = 138,590 square cm

the cost of painting the drum's inside and outside walls Rs. 0.15 x 138,590 = Rs20787

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4