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Tanzania [10]
2 years ago
6

Question 15 (1 point)

Mathematics
1 answer:
zloy xaker [14]2 years ago
4 0

Answer:

  • The value of k is 12.57
  • Radius of a seventeenth-century cannonball is 2.999 inches which can be rounded off to 3

Step-by-step explanation:

Let s be the surface area and r be the radius

Then according to given statement

s∝r²

Removing the proportionality symbol introduces k, the constant of proportionality

s = kr^2

Now

A soap bubble with a  0.75 in. radius has a surface area of approximately 7.07 square inches.

Putting in the equation

7.07 =  k (0.75)^2\\7.07 = k * 0.5625\\k = \frac{7.07}{0.5625}\\k = 12.5688..\\k = 12.57

The euqation beomes

s = 12.57r^2

Putting s = 113.1 in the equation

113.1 = 12.57r^2\\r^2 = \frac{113.1}{12.57}\\r^2 = 8.99761...\\\sqrt{r^2} = \sqrt{8.9976..}\\r = 2.9996..

Hence,

  • The value of k is 12.57
  • Radius of a seventeenth-century cannonball is 2.999 inches which can be rounded off to 3
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