Question

6. i) A road roller 140cm long and 77cm in diameter makes 300 revolutions to level a field
completely. Find the area of the field (in m²).
ii) The total surface area of cylinder is 2728cm”. Find the height of the cylinder if the radius of
the base is 7cm.​

Answer 1

Answer:

(1)Let us denote the road roller with cylinder.

Now the height of cylinder = 1.4m

Radius = 0.77/2 = 0.385m

Now area of field = CSA of cylinder × 300

:. Surface area of cylinder = 2 × π × r × h

= 2 × 22/7 × 0.385 × 1.4

= 44 × 0.385 × 0.2

= 8.8 × 0.385

= 3.388

therefore CSA of cylinder is 3.388 m^2

:. Area of field = 3.388 × 300 = 1016.4m^2

(2) TSA of cylinder = 2728cm^2

Radius = 7cm

Height = ??

Now,

TSA of cylinder = 2728

i.e. 2πr(h+r) = 2728

i.e. 2(22/7)(7)(h+7) = 2728

i.e. 44h + 308 = 2728

i.e. h =( 2728-308)/44

i.e. h = 2420/44 = 55

Therefore the height of the cylinder is 55 cm