SOLUTION: A circular disc of cast iron is 7 ft. in diameter and 1 1/3 in. thick. Determine weight. A plate 1 ft. square and 1 in. thick weighs 37.5 lbs. Area of circle: pi * r^2.

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Question 1208118: A circular disc of cast iron is 7 ft. in diameter and 1 1/3 in. thick. Determine weight.
A plate 1 ft. square and 1 in. thick weighs 37.5 lbs.
Area of circle: pi * r^2.
Not sure how to solve.
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
A circular disc of cast iron is 7 ft. in diameter and 1 1/3 in. thick. Determine weight.
A plate 1 ft. square and 1 in. thick weighs 37.5 lbs.
Area of circle: pi * r^2.
~~~~~~~~~~~~~~~~~~ 

              Step by step


(1)  Convert 7 ft to inches: 7 ft = 7*12 = 84 inches.



(2)  Find the area of the circular disk in square inches using the formula.
     Remember that the radius is half of the diameter.



(3)  Find the volume of the circular disk in cubic inches by multiplying its area 
     by the thick, which is 4/3 inches.



(4)  Find the density of the iron in    by dividing 37.5 lbs by the area 
     of 1 ft by 1 ft plate, which is 12*12 = 144 square inches.



(5)  To find weight, multiply the volume found in (3) by the density found in (4).

As you complete, celebrate your victory.


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comment from student: Please check my calculations :
1) 84 in. 2) 3.1416 * 42 * 42 = 5541.78 = 5542 in.^2 3) 5542 * 1.333 = 7380 in.^3
4) 37.5 / 144 = .2604 lbs. / ft.^3 5) 7389 * .2604 = 1924.09 = 1924 lbs


My response :   I checked your calculations.   They are correct.

I am very impressed.   My congratulations  !   You made great job  !



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

1 ft = 12 in
7 ft = 7*12 = 84 inches is the diameter, half that (42) is the radius
1 & 1/3 = 4/3
Volume of cylinder =
Volume of cylinder =
Volume of cylinder = cubic inches

"A plate 1 ft. square and 1 in. thick weighs 37.5 lbs"
means we have a 1 ft by 1 ft by 1 inch rectangular slab of iron
i.e. we have a 12 inch by 12 inch by 1 inch slab of iron
The volume of this would be length*width*height = 12*12*1 = 144 cubic inches.
144 cubic inches of iron weighs 37.5 pounds which will help set up a useful conversion factor.



=

=

=

This is the exact weight of the circular disc in terms of pi.

Here are some select approximations of this weight when we try various approximations of pi
rounding precisionpiweight
23.141923.25
33.1421924.475
43.14161924.23
53.141591924.223875
63.1415931924.2257125
73.14159271924.22552875
83.141592651924.225498125
93.1415926541924.225500575
103.14159265361924.22550033

As we use more decimal digits of pi, the weight seems to approach roughly 1924.2255 pounds.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


The methods shown by the other tutors are fine.

Here is another....

Start with the 37.5 pounds that the plate, 1 foot square and 1 inch thick, weighs.

The cross sectional area of the plate is 1 square foot.
The cross sectional area of the disc is .
The cross sectional area of the disc is greater than the cross sectional area of the plate by a factor of

The thickness of the plate is 1 inch; the thickness of the disc is 1 1/3 inches.
The disc is thicker than the plate by a factor of 1 1/3 = 4/3.

Multiply the weight of the plate by the factors by which the cross sectional area and thickness of the disc exceed those of the plate:

ANSWER: = 612.5pi = 1924 to the nearest whole number.
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