Question

2. The seniors at our high school decided to play a prank on the principal by completely filling his office with
basketballs. To determine the number of basketballs needed the students measured the room after moving out
the furniture. If the room measured 15 ft by 20 ft by 10 ft, approximately how many basketballs did the students
put in the principal's office? The basketballs had a circumference of 29 inches.
A. 56,000
B. 36,600
C. 12,600
D. 9,600

Answer 1

Answer:

C. 12,600

Step-by-step explanation:

You can try a rough approximation by finding the volume of the room, finding the volume of one basketball, an dividing the first volume by the second one. This method will give a large estimate since there will be empty space between the balls.

volume of room:

V = L * W * H = 15 * 20 * 10 ft^3 = 3,000 ft^3

volume of one ball:

circumference = 29 in.

From the circumference we find the radius.

circumference = 2(pi)r

2(pi)r = 29 in.

r = (29 in.)/(2pi) = 4.61549 in.

Now we convert inches to feet.

4.61549 in. = 4.61549/12 ft = 0.384624 ft

Now we use the radius of a ball in ft to find the volume of a ball in cubic feet.

V = (4/3)(pi)r^3 = (4/3)(3.14159)(0.384624 ft)^3 = 0.23834 ft^3

Now we divide the volume of the room by the volume of a ball.

number of balls = (3,000 ft^3)/(0.23834 ft^3) = 12,587

The closest answer is C. 12,600

Answer 2

The number of basketballs is 12600 if the room is measured 15 ft by 20 ft by 10 ft option (C) 12,600 is correct.

What is volume?

It is defined as a three-dimensional space enclosed by an object or thing.

It is given that:

The room measured 15 ft by 20 ft by 10 ft,

As we know, a rectangular prism can be defined as a six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.

Volume of room = 15x20x10 = 3000 cubic ft

The basketballs had a circumference of 29 inches.

The sphere can be defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

$\rm V = \dfrac{4}{3} \pi r^3$

The circumference of the sphere:

C = 2πr

29 = 2πr

r = 4.615 inch (the radius of sphere)

Or

r = 0.384 ft

Volume of the sphere

$\rm V = \dfrac{4}{3} \pi (0.384)^3$

V = 0.23718 cubic ft

Total number of basketballs = 3000/0.23718 = 126486

The above value is near 12600

Thus, the number of basketballs is 12600 if the room is measured 15 ft by 20 ft by 10 ft option (C) 12,600 is correct.

Learn more about the volume here:

https://brainly.com/question/16788902

#SPJ5