Weight - Similar Form

[Guest]

Two anchors are of similar form. The smaller anchor weighs 1100 lbs. The larger anchor is 2 1/7 times as long. Determine weight of the larger anchor.


How is the problem solved ? I don't how to begin.

[Guest]

[tex]1100 \times 2\frac{1}{7} = 1100 \times 2 + \frac{1100}{7}=\\= 2200 + 157.14 = 2357.14[/tex]

[Guest]

Thanks.

[Guest]

If the anchors have similar form then the length, width and height all follow the same ratio to the original.

Example .... a one inch cube is similar in form to a 10 inch cube.
Its length is 10 times, its width is 10 times, its height is 10 times the smaller one so its volume and its weight will be 10x10x10 = 1000 times the original.

So in your question the large anchor will be 1100 x (2 1/7) x (2 1/7) x (2 1/7) lbs in weight,

OR 1100 x (2 1/7)^3 = 10823.62 lbs weight.

[Guest]

Thank you.

[leesajohnson]

1100×2x1/7= 1100

1100×2+1100/7= 2200

2200 + 157.14 = 2357.14

[Guest]

Thanks.

[Guest]

NO....NO....NO......

leesajohnson posting of the solution is wrong.......

The simple example posted earlier above with the cube example is correct.......

If the anchors have similar form then the length, width and height all follow the same ratio to the original.....correct...
Example .... a one inch cube is similar in form to a 10 inch cube.......correct....
Its length is 10 times, its width is 10 times, its height is 10 times the smaller one so its volume and its weight will be 10x10x10 = 1000 times the original......correct.........OK.....

As a further example.......

If the anchor was a cube of 10 x 10 x 10 inches, then its volume would be 1000 cubic inches.

If the density of the material was 1.1 lbs per cubic inch then its weight would be 1100 lbs as per the orig. question.

If the sides of the larger anchor cube were 2 times the smaller then the sides would be 20 x 20 x 20 = 8000 cubic inches in volume.
and for a density of 1.1 the weight would be 8800 lbs

So the larger anchor cube is 2 x 2 x 2 = 8 times the weight of the smaller.

So for the question the larger anchor will weigh 1100 x 2 1/7 x 2 1/7 x 2 1/7 = 1100 x 9.84 = 10824 lbs weight.