Question

the circumference of the base of a cylinder is 122cm & its height is 65cm . fond the volume of the cylinder​

Answer 1

Answer:

Given :-

• The circumference of the base of a cylinder is 122 cm & its height is 65 cm.

To Find :-

• What is the volume of the cylinder.

Formula Used :-

$\clubsuit$ Volume of Cylinder Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Volume_{(Cylinder)} =\: {\pi}r^2h}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

First, we have to find the radius of the cylinder :

Given :

• Circumference of the base = 122 cm

According to the question by using the formula we get,

$\small \implies \bf Circumference\: of\: Base_{(Cylinder)} =\: 2{\pi}r$

$\implies \sf 122 =\: 2{\pi}r$

$\implies \sf 122 =\: 2 \times \dfrac{22}{7} \times r$

$\implies \sf 122 =\: \dfrac{44}{7} \times r$

$\implies \sf 122 \times \dfrac{7}{44} =\: r$

$\implies \sf \dfrac{854}{44} =\: r$

$\implies \sf 19.41 =\: r$

$\implies \sf\bold{\blue{r =\: 19.41}}$

Hence, the radius of the cylinder is 19.41 cm .

Now, we have to find the volume of the cylinder :

Given :

• Height = 65 cm
• Radius = 19.41 cm

According to the question by using the formula we get,

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

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times (19.41)^2 \times 65$

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times 376.7481 \times 65$

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times 24488.63$

$\implies \sf Volume_{(Cylinder)} =\: \dfrac{538749.86}{7}$

$\implies \sf\bold{\red{Volume_{(Cylinder)} =\: 76964.26\: cm^3}}$

$\small \sf\bold{\purple{\underline{\therefore\: The\: volume\: of\: the\: cylinder\: is\: 76964.26\: cm^3\: .}}}$