contestada

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.

Respuesta :

absor201

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

[tex]s = kr^2[/tex]

Now

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

Putting in the equation

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

The euqation beomes

[tex]s = 12.57r^2[/tex]

Putting s = 113.1 in the equation

[tex]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..[/tex]

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

Otras preguntas