Question

The total surface area of a cylinder is 40π cm².If height is 5.5cm then its base radius.​

Answer 1

Answer:

total surface area of a cylinder is 40π cm²

2π r ( r + h) = 40π

2 r ( r + 5.5) = 40

2r² + 11r = 40

2r² + 11r -40 = 0

2r² + 16r -5r -40 = 0

2r(r+8) -5(r + 8) = 0

(2r-5)(r+8)=0

from here

r can be 5/2 = 2.5

and

r can be -8

but it is not possible as Radius can't be negative

so

radius = 2.5cm

Answer 2

Given :

Total Surface Area of the cylinder (A) = 40π cm²

Height of the cylinder (h) = 5.5 cm

To Find :

Radius of the base

Solution :

We know, The total surface area of a cylinder = Area of curved surface + Area of circular bases.

∴     Total surface area = 2πr (h + r)

⇒           40π                 = 2πr (5.5 + r)

⇒            40                   = 2r(5.5 + r)

⇒            40                   =  11r + 2r²

⇒     2r² + 11r - 40          = 0

⇒    2r² + 16r -5r -40     = 0

⇒    2r(r+8) - 5(r + 8)     = 0

⇒    (2r-5)(r+8)              = 0

we get two values of r from here,

Either, r = $\frac{5}{2}$ = 2.5 cm      or,    r = -8 cm

As Radius can't be negative, so the value of r would be 2.5 cm.

Hence the base radius is found to be 2.5 cm.