Question

A cylindrical vessel contain 49. 896 litres of liquid. cost of painting its CSA at 2 paise/sq.cm is Rs. 95.04. then it's total surface area is what?​

Answer 1

Hey mate,.

Volume of cylindrical vessel= 49.896 L

= 49.896× 1000 = 49896 cm³

[ 1 L = 1000 cm³]

Cost of painting at 2 paise per square cm= ₹ 95.04

Curved surface area of cylinder= cost / rate

Curved surface area of cylinder=95.04/.02

Curved surface area of cylinder= 4752 cm²

Let r and h be the radius and height of the cylinder .

Curved surface area of cylinder= 2πrh

2πrh = 4752……..(1)

Volume of Cylinder= πr²h

πr²h= 49896 ……….(2)

From equation 1 and 2

2πrh/πr²h = 4752/49896

2/r = 594/6237

r= 21 cm

Put this value of r in eq 1

2πrh = 4752

2 × (22/7)× 21× h= 4752

2×22×3×h = 4752

h= 4752/2×22×3

h= 36 cm

Total surface area of the cylindrical vessel= 2πr(h+r)

= 2×(22/7)×21(21+36)

= 2×22×3(57)

= 7524 cm²

Hope it will help you

Answer 2

Solution: It is given that a cylindrical vessel contain 49. 896 litres.

Cost of painting its CSA at 2 paise/sq.cm = Rs. 95.04

Volume = 49.896 × 10000 cm^3

Therefore, πr^2h = 49,896 cm^3 .....(1)

[1L = 1000cm^3]

As we know that,

CSA of cylindrical vessel = Cost/rate

CSA of cylindrical vessel = 95.04/0.02 cm^2

Therefore, 2πrh = 4752 cm^2 ..........(2)

Let 'r' and 'h' be radius and height of the cylindrical vessel.

Now, for finding radius of cylindrical vessel, divide equation1 and equation 2:

Volume/CSA = 49,896/4752

=> πr^2h/2πrh = 49,896/4752

=> r/2 = 42/2

=> r = 21 cm.

Now, for finding height

Putting the value of 'r' in equation 2, we get:

CSA of cylindrical vessel = 4752

=> 2πrh = 4752

So,

Height, h = CSA/2πr

=> h = 4752/2 × 22/7 × 21

=> h = 4752 / 44 × 3

=> h = 4752 / 132

=> h = 36 cm.

Now,

TSA of of cylindrical vessel

= 2πr (r + h)

= 2 × 22/7 × 21 (21 + 36)

= 7524 cm^2.

Therefore, TSA of of cylindrical vessel is 7524 cm^2.