Answer:
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:
[tex]V=\frac{4}{3}\pi r^3[/tex]
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:
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (3.2)^3\\V=137.26[/tex]
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
