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Liono4ka [1.6K]
2 years ago
9

A cylinder is filled up with water to 3 4 its total capacity. The solid sphere is dropped completely into the cylinder. How high

up the container will the water reach after the sphere is fully submerged? Give your answer rounded to 1 DP.
Mathematics
1 answer:
Olenka [21]2 years ago
8 0

Answer:

30.3 cm

Step-by-step explanation:

Suppose the height is h after the sphere is full submerged.

4/3\piR³ = \pir²(h-30) The volume of the sphere is equal to the volume

4/3\pi x(10/2)³=\pi × (14/2)²(h-30)  of the water surface rising

4/3 × 125 = 49 × (h-30)

h - 30 = 49 × 3/4 × 125

h - 30 = 0.3

h = 30 + 0.3

h = 30.3 cm

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Answer:

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And replacing the info we got:

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So then the correlation coefficient would be r =0.1955

Step-by-step explanation:

Data given

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Solution

The correlation formula is given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have the following sums:  

n=9 \sum x = 530, \sum y = 243, \sum xy = 14615, \sum x^2 =32656, \sum y^2 =8245  

And replacing the info we got:

r=\frac{9(14615)-(530)(243)}{\sqrt{[9(32656) -(530)^2][9(8245) -(243)^2]}}=0.1955  

So then the correlation coefficient would be r =0.1955

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