Question

there is a rectangle is rotated on its length 'a' to form cylinder. If breadth of rectangle is ‘b’ then the volume of cylinder is:

Answer 1

First let us draw a diagram..

Answer 2

cylinder radius=b; height=a

Answer 3

\[V=\pi r^2h\]

Answer 4

The length of the rectangle will become the height for the cylinder.

Answer 5

there d is the diameter and h is the height for the cylinder

and in rectangle : a is the length of the rectangle and b is the breadth of the same figure.

Answer 6

Now as the total breadth of the rectangle will form the circumference of the base of the cylinder (circle)

we have : \(b = \textbf{circumference of the circle}\)

Answer 7

what do you get for "r" now in the terms of b ... @msingh ?

Answer 8

b^2/4

Answer 9

What is the formula for the circumference of a circle?

Answer 10

2pir

Answer 11

b/4

Answer 12

\(b = 2\pi r\)
\(r = \cfrac{b}{2\pi}\)

Check your method again @msingh .

Answer 13

k

Answer 14

So we have : \(r = \cfrac{b}{2\pi}\)

and \(h (\textbf{ height of the cylinder}) = a \)

and the formula for Volume of a cylinder = \(\pi \times r^2 \times h\)

Answer 15

We have both values. Can you do that now?

Just plug in the values.

Answer 16

yes
i got
(a *b^2)/pi

Answer 17

srry
(a *b^2)/4pi

Answer 18

Great work!

\(V = \pi \cfrac{b^2}{4\pi^2}a \)
\(V = \cancel{pi}^1 \cfrac{b^2}{4 \cancel{\pi^2}^{\pi} } a\)

Answer 19

@SheldonEinstein
thank u so much

Answer 20

You're welcome!