how do i find teh hight of a cylinder with the base dia of 500mm and the capacity of 250 liters?

Question

please help :D

Answer 1

The key thing is the relationship between length and volume in the metric system:

1 cm³ = 1 mL

So I'd suggest first converting everything either to cm³ or to mL.

I'll go with cm³:

250 L × (1000 mL/1 L) × (1 cm³/1 mL) = 250,000 cm³

So the volume of the cylinder is 250,000 cm³.

And the radius is 500/2 mm × (1 cm/10 mm) = 25 cm.

Then just use the formula for the volume of a cylinder.

V = πr²h

And you know V and r, so just solve for h.

250,000 cm³ = π(25 cm)²h = π(625 cm²)h

250,000 cm³ = π(625 cm²)h

250,000 cm³ = π(625 cm²)h

250,000 cm³/(625π cm²) = 400/π cm = h ≈ 127 cm

Re-checking...

V = πr²h = π(25 cm)²(400/π cm) = 625(400) cm³ = 250,000 cm³ × (1 cm³/1 mL) × (1 L/1,000 mL) = 250 L

So I think it's right.

Answer 2

You would have to first convert liters to cubic millimeters. 1 liter equals 1 million cubic millimeters. You have 250 liters, so you have 250 million cubic millimeters. The equation for volume is V = B x H, where V is volume, B is base area, and H is height of the cylinder. So you know volume, which is 250 million cubic millimeters. To find out base area of a circle multiply pi times radius squared. Radius is half of diameter so it would be 250mm. So area of your cylinder is 196,349.54mm squared. So now you know two out of three parts of your equation, volume and base. So transposing, you would have V/B = H. 250,000,000mm3 / 196,349.54mm2 = H. The two exponents cancel leaving you with 1273.24 mm which is you cylinder height. Hope this helps.

Answer 3

The diameter/2 is the radius
500/2=250mm

1 liter is 1000000 mm cubed
250 liters is 250 000 000 mm cubed

Formula for volume of cylinder:
pi * radius^2 * height = volume
pi * 250^2 * height = 250,000,000
height = 250,000,000/(pi * 250^2)
height = approximately 1273.24mm

Answer 4

V = π r ² h
d = 50 cm
r = 25 cm

250 x 1000 = π x 25² x h
h = (250 x 1000) / (π x 25²) cm
h = 127.3 cm