Question

The diameter of cylinder is 36 cm. and it's volume 14256 cubic cm. find height of cylinder? ​

Answer 1

Given

• Diameter of cylinder = 36cm
• Radius of cylinder = 36/2 = 18cm
• Volume of cylinder = 14256cm³

Find out

• Height of cylinder

Solution

As we know that

$\large{\purple{\boxed{\orange{\bigstar\bf{\red{Volume\:of\:cylinder=\pi{r^2h}}}}}}} \\ \\ \implies\tt 14256=\dfrac{22}{7}\times{(18)^2}\times{h} \\ \\ \\ \implies\tt 14256=\dfrac{22\times{324\times{h}}}{7} \\ \\ \\ \implies\tt h={ \dfrac{ \cancel{14256} \: {}^{44} \times 7}{22 \times \cancel{324} }} \\ \\ \\ \implies\tt h=\dfrac{44\times{7}}{22} \\ \\ \\ \implies\tt h=2\times7=14cm$

Hence,

• Height of cylinder is 14cm

Additional Information

• Total surface area of cylinder : 2πrh + 2πr²
• Curved surface area of cylinder : 2πrh

$\rule{200}3$

Answer 2

$\bigstar\:\:\rm\blue{ANSWER}\:\:\bigstar$

$\bigstar\:\:\rm\blue{GIVEN}\:\:\bigstar$

• The Diameter of the Cylinder is 36cm

• Radius=$\dfrac{\cancel{36}}{\cancel{2}}=18cm$

• The Volume of Cylinder is 14256cubic cm.

$\bigstar\:\:\rm\red{TO\:FIND}\:\:\bigstar$

• The Height of the Cylinder.

$\bigstar\:\:\rm\red{FORMULAE\:USED}\:\:\bigstar$

• ${\boxed{\bf{\blue{Volume\:of\: cylinder={\red{π r^{2}h}}}}}}$

Now,

Volume of Cylinder = πr²h.

$\implies\rm\blue{14256=\dfrac{22}{7}\times{(18)}^{2}(h)}$

$\implies\rm\blue{14256=\dfrac{22}{7}\times{324h}}$

$\implies\rm\blue{h=\dfrac{\cancel{14256}\times{7}}{\cancel{324}\times{22}}}$

$\implies\rm\blue{h=\dfrac{\cancel{44}\:^{2}\times{7}}{\cancel{22}}}$

$\implies\rm\blue{h=2\times{7}=14cm}$

Thus, The height of the cylinder is 14cm.

$\bigstar\:\:\rm\pink{MORE\:TO\:KNOW}\:\:\bigstar$

• Total Surface area of Cylinder=2πr(r+h)

• Lateral Surface area of Cylinder =2πrh.

• Volume of Cuboid= Length×Breadth× Height.