Ineed all the questions answered. show work

5 i)  Space occupied by 1 ball = 137.26 cubic centimeters

5 ii)  Space occupied by 6 tennis balls =  823.56 cubic centimeters

6 i)  19.2 centimeters

6 ii)  12.8 centimeters

6 iii) 6.4 centimeters

6 iv)  1572.86 cubic centimeters

7.  749.3 cubic centimeters

Step-by-step explanation:

5.

i)

A tennis ball is in a shape of a sphere. The space occupied by 1 tennis ball is the volume of a sphere. The formula is:

Where

V is the volume and r is the radius (half of diameter)

Given diameter is 6.4 , the radius would be:

r = 6.4/2 = 3.2

Now, we substitute and find the volume:

Space occupied by 1 ball = 137.26 cubic centimeters

ii)

We found space occupied by 1 ball, so space occupied by 6 balls would be 6 times that. So that would be:

Space occupied by 6 tennis balls = 137.26 * 6 = 823.56 cubic centimeters

6.

i)

The length of the box would be 3 diameters lined up. Since the length comprises of 3 balls side by side, we can say that 6 diameters would make up the length of the box, so:

diameter = 6.4

3 diameters = 6.4 * 3 = 19.2 centimeters

ii)

Now, we want the width of the box. That is 2 tennis balls lined up (as seen in the picture). That would be 2 diameters. so:

diameter = 6.4

2 diameters = 6.4 * 2 = 12.8 centimeters

iii)

The height of the box would be the height of 1 balls (see pic). That would be just 1 diameter of the ball. Given:

Diameter = 6.4 cm

So,

Height = 6.4 cm

iv)

The box is a rectangular prism. Which has a capacity (volume) formula as:

Volume = length * width * height

In the first 3 parts of this problem, we found each. Let's multiply each out to find the capacity of the box.

Volume = 19.2 * 12.8 * 6.4 = 1572.86 cubic centimeters

7.

The amount of empty space in the box is the volume of the rectangular box MINUS the volume of all the 6 balls. We have already found:

Volume of Box = 1572.86

Volume of 6 balls = 823.56

Hence,

Empty Space = 1572.86 - 823.56 = 749.3 cubic centimeters

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step-by-step explanation: