Mathematics, 03.12.2020 19:50 kaileyy06

Tennis balls with a diameter of 2.5 inches are sold in cans of three. The can is a cylinder. What is the volume of the space NOT occupied by the tennis balls? (Assume the tennis balls touch the can on all sides, top and bottom.) Round to the nearest tenth and show all steps and reasoning.

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Answer from: marziel24

The space NOT occupied by the tennis balls is 12.26 cube inches.

Step-by-step explanation:

The space NOT occupied = volume of cylinder - total volume of spheres

The can is cylinder with volume = $\pi$ $r^{2}$ h

where r is the radius and h the height of the cylinder

With the given condition,

r = $\frac{diameter}{2}$ = $\frac{2.5}{2}$

= 1.25 inches

h = 3 x diameter = 3 x 2.5

= 7.5 inches

So that,

Volume of the can = $\frac{22}{7}$ x $(1.25)^{2}$ x 7.5

= 36.830

Volume of can is 36.83 cube inches.

The tennis ball is a sphere with volume = $\frac{4}{3}$ $\pi$ $r^{3}$

= $\frac{4}{3}$ x $\frac{22}{7}$ x $(1.25)^{3}$

= 8.185

Volume of the tennis ball is 8.19 cube inches.

Since they are sold in three's, then;

total volume of the tennis balls = 3 x 8.19

= 24.57

Volume of the tennis balls is 24.57 cube inches.

Thus,

The space NOT occupied = 36.83 - 24.57

= 12.26

The space NOT occupied by the tennis balls is 12.26 cube inches.

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

step-by-step explanation:

times by times

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Tennis balls with a diameter of 2.5 inches are sold in cans of three. The can is a cylinder. What is...