A lathe cuts an 8” x 8” x 4’ steel square bar into a 6” x 4’ circular post, how much was removed?

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A lathe cuts an 8” x 8” x 4’ steel square bar into a 6” x 4’ circular post, how much was removed?

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Күн бұрын

How to find the volume of a rectangular solid and cylinder.
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Пікірлер: 31

@markfeeley9575 8 ай бұрын

Very little steel was removed before the interrupted cut broke the tool bit.

@terry_willis 8 ай бұрын

If your answer was correct here's a bonus question: How much steel was wasted by not using a 6"x6"x4' piece of stock. See correct answer below: \ \ \ \ \ \ \ \ \ \ Answer: 1344 cu"

@russelllomando8460 8 ай бұрын

had to research the cyl volume, but then got it. thanks for a great test.

@harrymatabal8448 5 ай бұрын

Ok. I am at the bar at the moment. As soon as I finish my drink I will listen to your long story. Have a shot on me

@peteroleary9447 8 ай бұрын

The question is poorly stated. Circular infers well, a circle. A circle is a 2 dimensional object with no volume. A "circular post" seems simple enough -- is it a round bar of a certain length? One would think so. If so, it would be called a cylinder, a 3 dimensional object. If you're dealing with geometric solid shapes, it's better to use normal nomenclature, like a machinist would. Two other issues: This scenario is highly implausible because no machine shop would make a 6" diameter bar from square stock. Round stock is just as available -- cutting it from square stock would mean that ~489 lbs. of steel would be wasted, not to mention several hours of cutting. A machinist would have to drill center holes in each end of the bar to support the bar in the lathe tailstock.

@mylittlepitbull3143 8 ай бұрын

Disagree. Very well stated.

@Herby-1620 3 ай бұрын

Many new calculators (like one for a mobile phone) have a "Pi" button which has many more decimal places.

@robertstuart6645 8 ай бұрын

The answer can also be expressed in cubic feet, namely 0.99 cu. ft.

@jald910 8 ай бұрын

You can take the area of the rectangular end 8 x 8” = 64 in squared The area of the circular end is 9 x pi, or 28.27. 64 less 28.27= 35.73 inches squared x 48 inches = 1715 in cubed

@decosse01 6 ай бұрын

I did it the same way - keep the 48 out of the initial arithmetic and just subract the areas THEN multiply by the length

@harrymatabal8448 5 ай бұрын

Find the volume of the square bar and subtract the volume of the circular bar

@roger7341 8 ай бұрын

Too much.

@TPJ79 8 ай бұрын

I'm no great mathematician but I thought the volume removed would be the volume of the circular post 1,356.48"³

@jamieoconnell127 8 ай бұрын

The answer is 1714.83 cubic inches. If you're going to give your answer to 2 decimal places, you need to use a much more precise estimation of pi (3.14159265359).

@larrystuder6378 8 ай бұрын

I did it in percent. In about 10 seconds , I got something more than 50 % of the area, and consequently of the volume. I know both A = s * s, and A= pi * r ^2. Too lazy to multiply it out in my head.

@tomtke7351 8 ай бұрын

GIVEN: START SIZE = 4ft×8in×8in square END SIZE = 4ft×6in diameter bar three steps: #1 calculate VOLUME (VOL.1) of beginning rectangular cube #2 calculate VOLUME (VOL.2) of circular rod after cutting. #3 VOL.removed = VOL.1-VOL.2 #1 START SIZE = 4ft×8in×8in VOL.1 = 8×8×4×12 = 3,072 in^3 #2 END SIZE = 4ft×6in diameter VOL.2 = pi×r^2×h = 3.1416x3^2×4×12 = 1,357.2 in^3 #3 VOL.removed = VOL.1 - VOL.2 = (3,072 - 1357.2)in^3 = 1,714.8 in^3 VERIFY the volume removed is the 2 dimensional square minus the inside circle all × the height square = 8×8 = 64 in^2 circle = pi×3^2 = 28.274 in^2 square - circle = 64 - 28.274 = 35.726 in^2 35.726in^2 × 12in/ft × 4ft = 1,714.8in^3 NOTE: when doing calculations like this for ◇homework ◇real work My approach is preferred... when attacking a test short cuts are required

@tomtke7351 8 ай бұрын

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@bobcornwell403 8 ай бұрын

I came up with approximately 1715 cubic inches.

@genelowry5666 6 ай бұрын

.99 ft^3

@Dale.121 8 ай бұрын

25%

@Evertb1 8 ай бұрын

Feel free to use a calculator? I am still searching for feet and inches on mine.

@advancedautomotivemachine4791 8 ай бұрын

Right up my alley :) 1714.83 cu in depending on how far out you want to run pi

@peterkennette9865 8 ай бұрын

1714 cu in.

@harrymatabal8448 5 ай бұрын

Would it not be easier to buy a circular bar. Why make life difficult

@richardl6751 8 ай бұрын

Lost nearly a cubic foot.

@henkhu100 6 ай бұрын

Because yoy use only two decimals for pi the answer is in fact not correct. If you use 3,14159 for pi the answer is less than 1,715 The number of decimals you use for pi also determines the number of accuracy you can use in the answer,

@Veronica.John10-10 8 ай бұрын

omg sometimes you give us the dumbest and simplest problems to solve that we can do in our heads, and then sometimes... THIS. You were feeling particularly sadistic today, weren't ya'? ;)