If the radius of a cylinder is increased by 25% and its height remains unchanged, then find the percent increase in volume.?

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

Given that , 2?rh = 264
and ?r²h = 924
? ( ?r²h) / (2?rh) = 924 / 264 = 7/2
? r/2 = 7/2
? r = 7
? d = 2r = 14 m
Also, 2 x (22/7) x 7 x h = 264
? h = 264 / 44 = 6
? d/h = 14/6 = 7/3 = 7 : 3

Let radii be 2r and 3r and heights be 5h and 3h.
? Ratio of volumes = [?(2r)² x 5h] / [?(3r)² x 3h]
= 20/27 = 20 : 27

Curved surface area of the cylinder = 2?rh
= 2 x (22/7) x 7 x 160
= 7040 sq cm

Let the height and radius and radius of solid cylinder be h and r cm respectively
Given that, radius (r) = 5 cm
and total surface area = 660 cm²
? 2?rh + 2?r² = 660
? 2?r(h + r) = 660
? (h + 5) = 330/5? = 330/5 x 7/22
? h = 66 x (7/22) - 5 = 21 - 5
? Required height = 16 cm

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)

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

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

Curved surface area = 2?rh
= 2 x (22/7) x 0.25 x 3.5
= 5.5 sq m
? Cost of painting 5.5 sq m = 10 x 5.5
= ? 55

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