Question

The curved surface area of a cylindrical building is 4400 cm2. Find its height if the radius is 35 cm.​

Answer 1

Answer:

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 rhCurved surface area of a cylinder=2πrh

Circumference\ of\ the\ cylinder\ base = 2\pi rCircumference of the cylinder base=2πr

Volume\ of\ the\ cylinder\ base =\pi r^{2} hVolume of the cylinder base=πr2h

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 = 3.14π=3.14

Put the values in the equation

110= 2\times 3.14\times r110=2×3.14×r

r = \frac{110}{6.28}r=6.28110

r = 17.52 cm (Approx)

Put in the curved surface area formula of a cylinder

4400= 2\times 3.14\times 17.52\times h4400=2×3.14×17.52×h

4400= 110.03\times h4400=110.03×h

h = \frac{4400}{110.03}h=110.034400

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 39.99Volume of the cylinder base=3.14×17.52×17.52×39.99

Volume\ of\ the\ cylinder\ base =38543.332\ cm^{3}Volume of the cylinder base=38543.332 cm3

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

Answer 2

Given,

The curved surface area = 4400 $cm^{2}$

Radius (r) = 35cm

To Find,

Height (h)

Solution,

We have the curved surface area of a cylindrical building as 4400 $cm^{2}$

and the radius given is 35 cm

we need to find the height of a cylindrical building

Curved surface area = 2 x $\pi$ x r x h

                     4400    = 2 x 3.14 x 35 x h

Further solving this equation we get,

                               h  =  $\frac{4400}{2 * 3.14 * 35}$

                               h  = 1.8198

Hence, The height of a cylindrical building is 1.82 cm