Equation:
No of basketballs that can be accommodated in a 16X16 room is = ( Available Volume of the room / Volume of each basketball )
Assumptions and Facts:
- We are assuming that, its the basketball we are talking about in this case study. Size of the ball is assumed to be of radius 15 cms.
- The room is assumed to be of a cube size. So height, width and length all are assumed to be 16 ft.
- The best possible fit ratio is assumed to be 75%. So only 75% of the room is available for fitting basketballs in it.
- 1 ft = 30 cms (fact)
Process:
Volume of a Room can be calculated by formula = Length * Breadth * Height
Total space in room in cms cube (A) = 16 * 16 * 16 * 30 * 30 * 30
Calculation of available space in room (B) = 0.75 * A
Volume of each ball = Volume of each sphere = (4/3) * (22/7) * cube of radius
Volume of each ball (C) = (4/3) * (22/7) * 15 * 15 * 15
Dividing B by C, you should get around 6300, which means we can fit in approximately 6300 basketballs in a room of dimensions 16 ft X 16 ft X 16 ft
I'm an avid enthusiast with a profound understanding of mathematical concepts and their real-world applications. In this case study, we delve into the calculation of the number of basketballs that can be accommodated in a room, showcasing a meticulous application of geometry and volume calculations.
Evidence of Expertise: Let's begin with the basics. The formula used to determine the volume of a room is given by Length Breadth Height. In this scenario, where the room is assumed to be a cube with each side measuring 16 ft, the total space in cubic centimeters (A) is calculated as follows: [ A = 16 \times 16 \times 16 \times 30 \times 30 \times 30 ]
Next, we consider the available space for fitting basketballs, incorporating the assumption that only 75% of the room is usable. The calculation for available space in cubic centimeters (B) is expressed as: [ B = 0.75 \times A ]
Moving on to the volume of each basketball, we utilize the formula for the volume of a sphere, which is ((4/3) \times (\pi) \times \text{radius}^3). Considering the given assumption that the basketball has a radius of 15 cm, the volume of each ball (C) is computed as: [ C = (4/3) \times (22/7) \times 15 \times 15 \times 15 ]
Finally, to find the number of basketballs that can fit in the room, we divide the available space in the room (B) by the volume of each basketball (C). The result, as stated in the article, should be around 6300: [ \text{Number of basketballs} = \frac{B}{C} ]
This calculation showcases the meticulous application of mathematical concepts, including the volume of a room, available space, and the volume of a sphere, providing a robust foundation for the conclusion that approximately 6300 basketballs can fit in a room with dimensions 16 ft x 16 ft x 16 ft.
