A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the covered surface of the pillar at the rate ? 10 per sq m .?

In one revolution, area covered = Covered surface area
? 2?rh = 2 x (22/7) x 42 x 120 = 31680 sq cm
in 500 revolutions,
Area covered = 31680 x 500 = (1584 x 10⁴) sq cm
= (1584 x 10⁴) / (10⁴) = 1584 sq m

Area of 4 wails = Lateral surface area perimeter = 2(l + b) = 250
? l + b = 250/2 = 125 m
Area to be painted = Cost/Rate = 15000/10 = 1500 sq m
Area of 4 wails = 2(l + b)h = 250 h
? 250h = 1500
? h = 1500/250 = 6 m

Here, A = -8%, B = 4%
According to the formula,
Net effect on volume = [2A + B + A² + 2AB/100 + A²B/100²]%
= [2 x (-8) + 4 + (-8)² + 2 x (-8) x 4 /100 + (-8)² x 4 /100²]
= [-16 + 4 + 64 - 64/100 + 256/10⁴]%
=[-12 + 0 + 0.0256]%
= -11.9744% (decrease)

According to the formula
Percentage increase in volume
= (2k + k²/100)% = ( 2 x 25 + 25²/100)%
= (50 + 625/100)% = (50 + 6.25)%
= 56.25%

According to the formula,
Percentage change in volume is directly proportional to the height,
So percentage decrease in volume = 8%

Volume of the cylinder = ?r²h
= (22/7) x 7 x 7 x 500 = 77000
= (77 x 10³) cm³

Curved surface area of right circular cone = ?rl
? 440 = (22/7) x 14 x l
? l = (440 x 7) / (22 x 14) = 10 cm

Given that,
Diameter of a right circular cone = 7 cm
? Radius of a right circular cone = 7/2 cm
and slant height of a right circular cone (l) = 10 cm
? Lateral surface area of a cone = ?rl = (22/7) x (7/2) x 10
= 11 x 10 = 110 cm²

Volume of cone = (1/3)?r²h
= (1/3) x (22/7) x 10 x 10 x 21 = 2200 cm³

Radius of cone (r) = 6/2 = 3 cm
and height of cone (h) = 4cm
Slant height (l) = ?h² + r²
= ?(4)² + (3)²
= ?16 + 9
= 5 cm
Now, curved surface area = ?rl
= (22/7) x 3 x 5
= 330/7 = 47 cm²