Of a spherical water ballon is filled with 113 millimeter ls of water, what is the appropriate radius of the ballon

r = -(-339/π)^(1/3)/2^(2/3) or r = (339/π)^(1/3)/2^(2/3) or r = ((-1)^(2/3) (339/π)^(1/3))/2^(2/3)

Step-by-step explanation:

Volume of the balloon is 113 ml=0.113 liters

1 liter= 1000 cm^3

the volume of the balloon in centimeters will be:

1000(0.113) = 113 cm^3

The radius of the balloon will be calculated as follows;

v=4/3πr³

plugging our values in the formula we get:

113=4/3πr³

solving for r we get

Solve for r:

113 = (4 π r^3)/3

113 = (4 π r^3)/3 is equivalent to (4 π r^3)/3 = 113:

(4 π r^3)/3 = 113

Divide both sides by (4 π)/3:

r^3 = 339/(4 π)

Taking cube roots gives (339/π)^(1/3)/2^(2/3) times the third roots of unity:

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| r = -(-339/π)^(1/3)/2^(2/3) or r = (339/π)^(1/3)/2^(2/3) or r = ((-1)^(2/3) (339/π)^(1/3))/2^(2/3)

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

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