Number - Lead Balls

[Guest]

A number of lead balls, with a diameter of 1/4 ", weighs 1 lb. Determine number.

Multiply the cube of the diameter, in in. or ft. , by the weight of a spherical in. or ft. of the composition.

The weight of a spherical in. of lead is .215 lbs.

My solution:

.25 x .25 x .25 = 0.015625 x .215 = 0.003359375

Where did I miscalculate ?

[Guest]

The volume of an object is proportional to its linear dimensions cubed

V = 4/3 x Pi x r^3 OR 4/3 x Pi x d^3 / 8

If a 1 inch ball weighs 0.215 lbs

then a 1/4 inch ball weighs 1/4 x 1/4 x 1/4 = 1/64 x 0.215 lbs = 0.215 / 64 ....(this is diameter cubed x weight)

and how many balls in 1 lb = 1 / (weight of one ball) = (64 / 0.215) = 297.67 balls = 297 balls

[Guest]

Thanks again.

[Guest]

Just a simple question to see if you are following the logic ??? .....

If a 1inch diameter ball weighs 1/4 lbs. how many 1/4 inch diameter balls are there in 1 lb weight of 1/4 inch diameter balls. ?

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[Guest]

4 ?

[Guest]

If you are following the logic then show your working out, each step.

[Guest]

I don't know.

[Guest]

Work it out using the same method as used in the original question.

[Guest]

My attempt:

I used a proportion -

1/.215 = .25/x (If an inch ball weighs .215 lbs., how many lbs. does a 1/4 in. ball weigh)

x = 0.05375 lbs.


1/4 x 1/4 x 1/4 = 1/64 x 0.05375 = 0.05375 / 64

64 / 0.05375 = 1190.69 = 1190 balls

I don't think that is correct.

[Guest]

Don't mix up the 2 problems......

This is the one I posed ..... It is based on the original but the figures are more simple......
do it using the same method as I used in the original solution....but the figures works out easier....
In this case a 1 inch dia ball weigh a 1/4 lbs NOT .215 lbs

" Just a simple question to see if you are following the logic ??? .....

If a 1inch diameter ball weighs 1/4 lbs. how many 1/4 inch diameter balls are there in 1 lb weight of 1/4 inch diameter balls. ? "

[Guest]

1/4 x 1/4 x 1/4 = 1/64 x .25 = 0.00390625 lbs.

64 / 0.00390625 = 16384 balls

If that is not correct, I don't know.

[Guest]

I think it should be:

1 x 1 x 1 x .25 = .25 lbs.

16 oz. x .25 = 4 oz.

16 / .25 = 64 balls

? ?

I can't solve it.

[Guest]

If you want to learn, there is no point in just asking questions. You need to try the questions yourself and try to follow the reasoning given in other similar examples. This question was not hard.....and as you can see I do it the same method as I used in the earlier question....

If a 1inch diameter ball weighs 1/4 lbs. how many 1/4 inch diameter balls are there in 1 lb weight of 1/4 inch diameter balls. ? "

As the question says the 1 inch ball weighs 1/4 lbs
and the 1/4 inch balls each have a weight of 1/4 x 1/4 x 1/4 = 1/64 of the weight of the 1 inch ball
So the weight of the 1/4 inch ball is 1/64 x 1/4 = 1/256 lbs

So number of 1/4 inch balls in 1 lb weight is.... 1 / (1/256)
turn upside down and multiply gives 256 / 1 = 256 balls
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[Guest]

Thanks. It is hard for me.