Question

5. The volume of a cylinder is 5544 cm and its height
is 16cm. Find its radius and its curved surface area..​

Answer 1

$\underline{ \underline{ \Large \bf { Given:} } }$

• Volume of a cylinder is 5544 cm³

• Height of the cylinder = 16 cm

$\underline{ \underline{ \Large \bf { To \: calculate:} } }$

• Radius of the cylinder

• C.S.A of the cylinder.

$\underline{ \underline{ \Large \bf { Calculation:} } }$

As we know that,

⇒ Volume of the cylinder = πr²h

According to the question,

⇒ 5544 = $\sf { \dfrac{22}{7} }$ × r² × 16

⇒ 5544 × 7 = 22 × r² × 16

⇒ 38,808 = 22 × r² × 16

⇒$\sf { \dfrac{38,808}{22} }$ = r² × 16

⇒1764 = r² × 16

⇒$\sf { \dfrac{1764}{16} }$ = r²

⇒$\sf { \sqrt{\dfrac{1764}{16} }}$ = r

⇒$\sf { \dfrac{\sqrt{1764}}{\sqrt{16}} }$ = r

⇒$\sf { \dfrac{42}{4} }$ = r

⇒ $\pmb { \rm \red{ 10.5 \:cm = r} }$

Henceforth, radius is 10.5 cm.

⇒ C.S.A of the cylinder = 2πrh

⇒ C.S.A of the cylinder = [ 2 × $\sf { \dfrac{22}{7} }$ × $\sf { \dfrac{42}{4} }$ × 16 ] cm²

⇒ C.S.A of the cylinder = [ 2 × 22 × 6 × 4 ] cm²

⇒ C.S.A of the cylinder = [ 44 × 24 ] cm²

⇒ $\pmb { \rm \red{ C.S.A_{(Cylinder)} = 1056 \: {cm}^{2} }}$

Therefore, C.S.A of the cylinder is 1056 cm².