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Question 15 (1 point)

The surface area of a sphere varies directly with the square of its radius. A soap bubble with a
0.75 in. radius has a surface area of approximately 7.07 square inches. Find the value of k, and
then find the radius of a seventeenth-century cannonball that has a surface area of 113.1
square inches.

1 Answer

7 votes

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

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 = (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 = (113.1)/(12.57)\\r^2 = 8.99761...\\√(r^2) = √(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
User Sivaramakrishnan
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