Question

The ratio of the height and diameter of a simple circular cylinder is 3: 2. Its entire surface area is 1232 sq. Cm. However, determine the height of the cylinder and the diameter of the ground​

Answer 1

Given that height of the cylinder is 8 cm and volume is 1232 cm ³

We know that the volume of the cylinder =πr ²

h

So,

1232=22/7×r×r×8

r² =1232×7/8

r=7 cm

Also we know that curved surface area of cylinder =2πrh

So,

Curved surface area =2×22/7×7×8

Curved surface area =252 cm ²

We know that total surface area of cylinder =2πr(r+h)

So,

Total surface area =2×22/7×7(7+8)

Total surface area =2580 cm²

Answer 2

Step-by-step explanation:

ratio of height and diameter =3:2

therefore, let height = 3x & diameter = 2x

or radius = 2x/2 = x

now, TSA of cylinder = 2πr(r+h)

1232 = 2*3.14*x(x+3x)

1232 = 6.28*4 x^2

1232 = 25.12 x^2

1232/25.12 = x^2

x^2 = 49.04 ≈ 49

x =√49

»[x = 7]

therefore, height = 3x = 3*7 = 21

& diameter = 2x = 2*7 = 14.