Question

Find the area of the base circle in the cylinder of height 15 cm and volume 600 cu. cm ?

Answer 1

Step-by-step explanation:

Given:-

In a Cylinder

• Height=15cm
• volume=600 cm^3

To find:-

The area of the vase circle in the Cylinder

Solution:-

Let radius=r

• As we know that in a Cylinder

${\boxed{Volume={\pi}r {}^{2}h}}$

• Substitute the values

${:}\longmapsto$$600={\dfrac {22}{7}}×{15}^{2}×h$

${:}\longmapsto$$600={\dfrac {22}{7}}×r {}^{2}×15$

• Now interchange both sides and get r

${:}\longmapsto$${r}^{2}={\dfrac {{\cancel {600}}×7}{22×{\cancel {15}}}}$

${:}\longmapsto$$r {}^{2}={\dfrac {280}{22}}$

${:}\longmapsto$$r {}^{2}=26.36$

${:}\longmapsto$$r={\sqrt {26.36}}$

${:}\longmapsto$$r=5.1cm$

• Now The base of Cylinder is a circle
• where r=5.1cm

as we know that in a Circle

${\boxed{Area={\pi}{r}^{2}}}$

• Substitute the values

${:}\longmapsto$$Area={\dfrac {22}{7}}×{5.1}^{2}$

${:}\longmapsto$$Area={\dfrac {22}{7}}×26.3$

${:}\longmapsto$$Area={\dfrac {22×263}{7×10}}$

${:}\longmapsto$$Area=8265.7cm {}^{2}$