1) The volume of the beach ball when fully inflated is 47690 cubic centimeters.
2) The value of x is 3.
Step-by-step explanation:
It is given that, an inflatable beach ball has a circumference of 141.3 centimeters.
1) To find the volume of the beach ball :
Use the formula for volume of sphere to find the volume of beach ball when fully inflated.
Volume of sphere = (4/3)πr³
where, r is the radius of the sphere and π has the default value of 3.14.
To find the radius :
The given circumference is 141.3 = 2πr
⇒ r = 141.3 / 2π
⇒ r = 141.3 / (2×3.14)
⇒ r = 141.3 / 6.28
⇒ r = 22.5
Now, substituting r= 22.5 in the volume of sphere formula
Volume of sphere = (4/3) ×3.14× (22.5)³
⇒ 4/3 ×3.14 ×11391
⇒ (12.56×11391) / 3
⇒ 47690 cubic centimeters
The volume of the beach ball when fully inflated is 47690 cubic centimeters.
2) The given equation is [tex]4^{x} = 64[/tex]
⇒ 64 = 4×4×4
⇒ 64 = 4³
Therefore, the value of x is 3.
