Question

a rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways by rolling the paper along its length or by rolling it along its breadth. find the ratio of their volumes of two cylinders thus form

Answer 1

The ratio of their volumes of two cylinders is 5:3

Step-by-step explanation:

Given:- A rectangular Sheet of,

Length=30 cm, Breadth=18 cm.

To find:- Ratio of Volumes of two cylinders = ?

Solution:-

On rolling the paper along the length,

height (h)  of cylinder = 18 cm,

radius (r) of cylinder = 15 cm.

Now,

Volume of cylinder (V) = $\pi r^{2} h$

$V=3.14\times 15^{2} \times18$ ----------($\pi =3.14$)

$V=3.14\times 15\times 15\times 18$

Volume of cylinder on rolling along length = $3.14\times 15\times 15\times 18$ sqcm. --------(equation 1)

Now, on rolling paper along its breadth,

height (h) of cylinder = 30 cm,

radius (r) of cylinder = 9 cm.

Now,

Volume of cylinder (V) = $\pi r^{2} h$

$V=3.14\times 9^{2} \times 30$ --------($\pi =3.14$)

$V=3.14\times 9\times 9\times 30$

Volume of cylinder on rolling along breadth = $3.14\times 9\times 9\times 30$ sqcm. ---------(equation 2)

Now, from equation 1 and equation 2,

$Ratio=\frac{equation\ 1}{equation\ 2}$

$Ratio=\frac{3.14\times 15\times 15\times 18}{3.14\times 9\times 9\times 30}$

$Ratio=\frac{15}{9}$

$Ratio=\frac{5}{3}$

Therefore ratio of cylinder after rolling paper length wise and breadth wise is 5:3.

Answer 2

Answer:

hi there

Step-by-step explanation:

The ratio of their volumes of two cylinders is 5:3

Step-by-step explanation:

Given:- A rectangular Sheet of,

Length=30 cm, Breadth=18 cm.

To find:- Ratio of Volumes of two cylinders = ?

Solution:-

On rolling the paper along the length,

height (h)  of cylinder = 18 cm,

radius (r) of cylinder = 15 cm.

Now,

Volume of cylinder (V) =  

----------()

Volume of cylinder on rolling along length =  sqcm. --------(equation 1)

Now, on rolling paper along its breadth,

height (h) of cylinder = 30 cm,

radius (r) of cylinder = 9 cm.

Now,

Volume of cylinder (V) =  

--------()

Volume of cylinder on rolling along breadth =  sqcm. ---------(equation 2)

Now, from equation 1 and equation 2,

Therefore ratio of cylinder after rolling paper length wise and breadth wise is 5:3.