Question

the curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110 cm. find the height and the volume of the cylinder

Answer 1

hope this helps.......

Answer 2

Answer:

The height of the cylinder is 39.99 cm and volume of the cylinder is 38543.332 cm³ .

Step-by-step explanation:

Formula

$Curved\ surface\ area\ of\ a\ cylinder = 2\pi rh$

$Circumference\ of\ the\ cylinder\ base = 2\pi r$

$Volume\ of\ the\ cylinder\ base =\pi r^{2} h$

Where r is the radius and h is the height .

As given

The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm.

$\pi = 3.14$

Put the values in the equation

$110= 2\times 3.14\times r$

$r = \frac{110}{6.28}$

r = 17.52 cm (Approx)

Put in the curved surface area formula of a cylinder

$4400= 2\times 3.14\times 17.52\times h$

$4400= 110.03\times h$

$h = \frac{4400}{110.03}$

h = 39.99 cm (Approx)

Therefore the height of the cylinder is 39.99 cm .

Put in the formula of volume of a cylinder .

$Volume\ of\ the\ cylinder\ base =3.14\times 17.52\times 17.52\times 39.99$

$Volume\ of\ the\ cylinder\ base =38543.332\ cm^{3}$

Therefore the height of the cylinder is 39.99 cm and volume of the cylinder is 38543.332 cm³ .