A problem related to simple algebra.?

Question

The cost of a stone linearly varies with square of it's Diameter. The cost of a 20 mm dia stone is 40000$. if the stone is broken into 3 parts & its ratios of radius are 5 : 3 : 2 . Calculate the loss in cost due to the breakage.

Answer 1

question is not proper.

Answer 2

Consider d1,d2,d3 are the diameters of the three pieces.
By condition: d1:d2:d3 =2( 5:3:2)=10:6:4
By other condition: C=K*D^2 where C=cost, D= diameter of the stone, K= constant of variation.
Therefore, $40000 = K*20^2
or, K=( 40000/400) = 100
Cost of the stone of 10mm dia.=K*10^2=100*100=$10000
Cost of the stone of 6mm dia =100*6^2=$3600
Cost of the stone of 4 mm dia = 100*4^2=$1600
cost of the three pieces =$15200
Loss =$40000-$15200 =$24800.

Answer 3

The question is a little unclear. If you inscribe 3 circles inside a bigger circle you get one answer. If you place them along a diameter, you get another answer.

I'll assume you mean that you place them along the diameter of the original stone.

You go from a 10mm radius stone (100 pi), to three stones with 5mm, 3mm and 2mm (25 pi, 9 pi, 4 pi). The ratio between the original and the sum of the other three is 100 : (25 + 9 + 4)

This is 100 : 38

Using similar ratios 40000$ would now be worth 38/100 or 15200$

Answer 4

cost = k*d^2
40000 = k*20^2
Thus k = 100
ie cost = 100d^2
Ratio of radii = ratio of diameters = 5 : 3 : 2 (= 10 : 6 : 4)

Thus the worth of the 10 mm stone is 100*10^2 ie $10000
The worth of the 6 mm stone is 100*6^2 ie $3600
and the worth of the 4 mm stone is 100*4^2 ie $1600

So the total worth of the 3 stones is $15200
whence the loss in value is $24800

Answer 5

The diameters of three pieces are 10mm, 6mm and 4 mm. The cost of all three pieces come to 15200 $ as compared to the cost of whole stone of 20 mm dia. The loss in cost is 24800$

Answer 6

the answer is not so simple
assuming the 3 new stones are all circles, you have to compute the max. radii of 3 circles fitting into the original circle, which is 20 mm. dia. and having diameters that relate at 5:3:2.
if you draw the diagram you'll see it's not simple at all

Answer 7

According to your question, the stone must be in the shape of a sphere or a cylinder (since you have mentioned the diameters). So if the stone is broken into peaces, It looses its value completely. Because it looses its shape.

Answer 8

the first stone is half the radius of the original, so the price will be half the original, so $20000.

the second stone is one third the radius of the original, so the price will be one third of the original, so $13333.33

the third is one tenth of the radius, so the price will be $4000

in total, the three stones will be worth $37333.33. the loss is 40000-37333.33 = $2666.67

Answer 9

20mm=40000
1mm=40000/20
1mm=2000
5:3:2=5x:3x:2x
so 5x+2x+3x=20
10x=20
x=2
5x=5*2=10mm=10*2000=20000$
2x=2*2=4mm=4*2000=8000$
3x=3*2=6mm=6*2000=12000$
so total amount=20000+8000+12000
=40000
so loss in cost =0

Answer 10

sorry