Question

The curved surface area and base area of a cylinder is same,prove that its height is equal to radius.

Answer 1

Step-by-step explanation:

With this height of a cylinder calculator you can now quickly use ten various height of a cylinder formulas which can be derived directly from the above equations:

Given radius and volume: h = V / (π * r²) ,

Given radius and lateral area: h = A_l / (2 * π * r) ,

Answer 2

For cylinder, we have

base radius=r, height=h

∴S

1

=Curved surface=2πrh

For cone, we have

l=

r

2

+h

2

and, S

2

=πrl=πr

r

2

+h

2

We have,

S

2

S

1

=

5

8

⇒

πr

r

2

+h

2

2πrh

=

5

8

⇒

r

2

+h

2

2h

=

5

8

⇒

r

2

+h

2

4h

2

=

25

64

⇒25h

2

=16r

2

+16h

2

⇒9h

2

=16r

2

⇒3h=4r

⇒

h

r

=

4

3

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