Question

the curved surface area of a cylindrical pole is 625 cmsquare and its volume is 824cm cube.find the diameter and height of the pole

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The diameter of pole is 5.28 cm and height of the pole is 37.67 cm.

Step-by-step explanation:

Given:

Curved Surface area of cylinder = 625 sq. cm

Volume of cylinder = 824 cubic cm.

We need to find the diameter and height of the pole.

Now we know that Curved Surface area of cylinder is given by 2 times π times radius (r) times height(h).

framing in equation form we get;

Curved Surface area = $2\pi rh$

Substituting the given value we get;

$2\pi rh =625\\\\\pi rh = \frac{625}{2} \ \ \ \ equation \ 1$

Also we know that Volume of the cylinder is given by π times square of radius (r) times height(h).

framing in equation form we get;

Volume of cylinder = $\pi r^2h$

Substituting the given value we get;

$\pi r^2h = 824\\\\\pi rh\times r =824$

Now Substituting the value of  π (r) (h) from equation 1 in above equation we get;

$\frac{625}{2} \times r =824\\ \\r = \frac{824\times 2}{625} = 2.64\ cm$

Now radius = 2.64 cm

diameter = $2\times radius =2\times2.64 = 5.28\ cm$

Now we will substitute value of r in equation 1 we get;

$\pi rh =\frac{625}{2}\\\\h = \frac{625}{2\times \pi \times 2.64}= 37.67\ cm$

Hence The diameter of pole is 5.28 cm and height of the pole is 37.67 cm.