Weigh - Plate

[Guest]

A brass plate has the following description:

1.5 in. thickness

Semi - circular in shape

Radius - 12 in.

4 holes - .75 in. in diameter

Brass weighing .3031 lbs. per cu. in., calculate weight of plate.


My attempt -

Area of semicircle - .5 x pi x r^2

.5 x 3.1416 x 12 x 12 = 226.1952 = 226 cu. in.

Volume - 226 x 1.5 = 339 cu. in.

339 - 9.4248 (circumference of 4 holes) = 329.5752 = 330 in.

330 x .3031 = 100.023 = 100 lbs.

I don't think that is correct - where did I miscalculate ?

[Guest]

Error on post:

Subject should read: Weight - Plate

[Guest]

339 - 9.4248 (circumference of 4 holes) = 329.5752 = 330 in.

It should be the area of the holes you take away not the circumference

But you did not calc that correct anyhow.

you seem to have calc Pi x radius x 4

The area of 4 holes is Pi x "Radius squared" x 4

[Guest]

3.1416 x 0.375 x 0.375 x 4 = 1.76715 (area of 4 holes)

339 - 1.76715 = 337.23285 (volume)

337.23285 x .3031 = 102.21528 = 102 lbs.

Correct ?

[Guest]

Correct

[Guest]

Thanks.

A question -

So, the holes would not be considered a cylinder ?

[Guest]

Yes the holes need to be considered as cylinders having a volume to take away.
It is the hap-hazzard way you do the question.....I am only reading your solution so I missed it.

3.1416 x 0.375 x 0.375 x 4 = 1.76715 (area of 4 holes)
Now multiply area by the thickness to get the volume of the holes....

339 - (volume of the holes) = (volume of the brass plate) (volume)

(volume of brass plate) x .3031 = (Weight of brass plate) = xxxxxxxxx lbs.


OR you could have worked out the area of the brass plate by (area of full semicirdle - area of 4 holes) = area of brass plate
then multiply by thickness to get volume...
then multiply by .3031 to get weight.

[Guest]

3.1416 x 0.375 x 0.375 x 4 = 1.76715 (area of 4 holes)

1.76715 x 1.5 = 2.650725 (volume of holes)

339 - 2.650725 = 336.349275 (volume of plate)

336.349275 x .3031 = 101.94746 = 102 lbs.

Correct ?

[Guest]

Yes, correct this time

[Guest]

Thanks.

This one also:

Area of semicircle - .5 x pi x r^2

.5 x 3.1416 x 12 x 12 = 226.1952 = 226 cu. in. (total area of plate)

3.1416 x 0.375 x 0.375 x 4 = 1.76715 (area of 4 holes)

226 - 1.76715 = 224.232 = 224 (area of plate)

224 x 1.5 = 336 (volume of plate)

336 x .3031 = 101.8416 = 102 lbs.

[Guest]

Yes, same answer, both methods are correct

[Guest]

Thanks again.