Question

doubt this question ​

Answer 1

Answer:

Question :-

• A rectangular sheet of paper measuring 66 cm by 20 cm is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.

Given :-

• A rectangular sheet of paper measuring 66 cm by 20 cm is rolled along its length to form a cylinder.

To Find :-

• What is the volume of the cylinder.

Solution :-

First, we have to find the radius :

Let,

$\mapsto \bf Radius =\: r\: cm$

Given :

• Length of sheet = 66 cm

According to the question by using the formula we get,

$\implies \bf Circumference_{(Circle)} =\: 2{\pi}r$

$\implies \sf 2{\pi}r =\: 66$

$\implies \sf 2 \times \dfrac{22}{7} \times r =\: 66$

$\implies \sf \dfrac{44}{7} \times r =\: 66$

$\implies \sf r =\: \dfrac{66 \times 7}{44}$

$\implies \sf r =\: \dfrac{462}{44}$

$\implies \sf\bold{\purple{r =\: 10.5\: cm}}$

Hence, the radius is 10.5 cm .

Now, we have to find the volume of cylinder :

Given :

• Height = 20 cm
• Radius = 10.5 cm

According to the question by using the formula we get,

$\implies \bf Volume_{(Cylinder)} =\: {\pi}r^2h$

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times (10.5)^2 \times 20$

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times (10.5 \times 10.5) \times 20$

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times 2205$

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{\cancel{48510}}{\cancel{7}}$

$\implies \sf\bold{\red{Volume_{(Cylinder)} =\: 6930\: cm^3}}$

$\therefore$ The volume of a cylinder so formed is 6930 cm³ .