Question

A rectangular sheet of paper is rolled along its length to make a cylinder. The
sheet is 33 cm long and 32 cm wide. A circular sheet of paper is attached to the
bottom of the cylinder formed. Find the capacity of cylinder so formed.
​

Answer 1

GiveN :-

A rectangular sheet of paper is rolled along its length to make a cylinder. The sheet is 33 cm long and 32 cm wide.

Therefore

• Height of cylinder = 32 cm

• Circumference of cylinder = 33 cm

To FinD :-

• Volume of the cylinder

SolutioN :-

$\large \longrightarrow \boxed{ \bf \orange{ Circumference = 2\pi r}}$

$\longrightarrow \sf 33 = 2 \times \frac{22}{7} \times r \\ \\\longrightarrow \sf r = \frac{33 \times 7}{22 \times 2} \\ \\\longrightarrow \sf r = \frac{231}{44} \\ \\\longrightarrow \sf r = 5.25$

Now Volume of the cylinder

$\large\longrightarrow \boxed{ \bf \blue{ Volume = {\pi r}^{2}h}}$

$\longrightarrow \sf Volume = \frac{22}{7} \times 5.25 \times 5.25 \times 32 \\ \\ \longrightarrow \sf Volume = \frac{19404}{7} \\ \\\longrightarrow \boxed{ \sf \green{ Volume = 2772 \: {cm}^{3}}}$

Answer 2

$\huge{\tt{\underline{\purple{Answer♡}}}}$

Given : Length of the rectangular sheet = 33 cm

And, Width of the rectangular sheet = 32 cm

As we know that,

length of the rectangular sheet = circumference of the circle

Circumference of the circle = 2πr

⇒ 33 cm = 2*22/7*r

⇒ r = (33*7)/(22*2)

⇒ r = 231/44

⇒ r = 5.25 cm

Capacity or volume of the cylinder = πr²h

⇒ 22/7*5.25*5.25*32

⇒ 22/7*27.5625*32

⇒ 19404/7

⇒ 2772 cm³

Hence, the capacity or the volume of the cylinder is 2772 cm³.

$\huge{\underline{\sf{\pink{Thanks}}}}$