Question

the curved surface area of a cylinder pillar is 264msqr and it's volume is 924msqr. the ratio of its diameter to its height is----​

Answer 1

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Given:

The curved surface area of a cylinder pillar is 264m² and its volume is 924m³.

To find:

The ratio of its diameter of its height.

Explanation:

Formula of the curved surface area of cylinder: 2πrh   [sq. units]

Formula of the volume of the cylinder: πr²h       [cubic units]

We have,

• Curved surface area of the cylinder:

→ 2πrh = 264

→ πrh = $\cancel{\frac{264}{2} }$

→ πrh = 132m².................(1)

• Volume of the cylinder:

→ πr²h = 924m³

→ (πrh) × r= 924

from equation (1), putting the place of (πrh),we get;

⇒ 132m² × r= 924m³

⇒ r= $\cancel{\frac{924m^{3} }{132m^{2} } }$

⇒ r= 7m

Therefore,

Diameter= 2 × r

Diameter= (2 × 7)m

Diameter= 14m.

Now,

• Height of the pillar:

→ 2πrh = 264

→ 2 $\frac{22}{7}$ × 7m × h = 264

→ $\frac{44}{\cancel{7}} *\cancel{7}*h\:=\:264$

→ h= $\cancel{\frac{264}{44} }m$

→ h= 6m.

The ratio of their diameter and height of the pillar;

⇒ 14m :6m

⇒ 7m : 3m