Question

1. An inflatable beach ball has a circumference of 141.3 centimeters. What is the volume of the beach ball when fully inflated? Record your answers in cubic centimeters, round to the nearest whole number. Use 3.14 for pie.
2. Which exponent can be substituted for the letter x to make the equation true?
4^x=64

Answer 1

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 $4^{x} = 64$

⇒ 64 = 4×4×4

⇒ 64 = 4³

Therefore, the value of x is 3.