|
Question 1189053: The core of a cast iron piece has the shape of a spherical segment of two bases. The radii of the upper and lower bases are 31 cm and 91 cm, respectively. The distance between the bases is 91 cm. find the weight of the core assuming that sand weighs 1600 kg per cubic meter.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Refer to this page for more info about spherical segments
https://mathworld.wolfram.com/SphericalSegment.html
We'll use formula (14) on that page
Plug in a = 31, b = 91, h = 91
a,b are the two radii of each parallel circular face.
h is the height of the spherical segment (aka the distance between the two circular faces)
 approximately. I used my calculator's stored version of pi.
The spherical segment has volume of roughly 1,715,643.12128009 cm^3
1 m = 100 cm
(1 m)^3 = (100 cm)^3
1 m^3 = 1,000,000 cm^3
One cubic meter represents 1 million cubic centimeters.
Because of this conversion factor, we'll divide that volume we found earlier by 1,000,000 to convert to cubic meters.
1,715,643.12128009 cm^3 = (1,715,643.12128009/1,000,000) = 1.7156431212801 m^3
The volume of this spherical segment is approximately 1.7156431212801 m^3
1 cubic meter = 1600 kg
1.7156431212801*1 cubic meter = 1.7156431212801*1600 kg
1.7156431212801 cubic meter = 2745.02899404817 kg
Answer: Approximately 2745.02899404817 kg
For the sake of comparison, a small car weighs about 1700 kg
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Since kilograms are just long time NOT the unit for weight (and not the unit for force, in general),
you must convert kilograms to newtons.
|
|
|
| |
