Question

curved surface area of a cylinder is 264 m square and its volume is 924 metre cube find the ratio of height and its diameter

Answer 1

Curved Surface Area of cylinder = 264 m²

Volume of the cylinder = 924 m³

To be found :

The height and diameter of the cylinder

Curved Surface Area of cylinder = 264 m²

$\rightarrow 2\pi rh=264\\ \rightarrow2\times \frac{22}{7}\times rh =264\\\rightarrow \frac{44}{7}\times rh=264\\\rightarrow rh=264\times\frac{7}{44}\\\rightarrow rh = 42$

Now,

Volume of the cylinder = 924 m³

$\rightarrow \pi r^{2}h=924\\\rightarrow \frac{22}{7}\times r \times r \times h = 924\\\rightarrow \frac{22}{7}\times 42\times r=924\: \: \: \: \: \: [as \: \:rh=42]\\\rightarrow 132 \times r=924\\\rightarrow r=\frac{924}{132}\\\rightarrow r=7$

Therefore

r(radius) = 7m

And

Height(h) = rh = 42

⇒ 7 × h = 42

⇒ h = 42 ÷ 7

⇒ h = 6m

∴diameter = 2r = 2×7 = 14m