To find the empty space in the container, we need to calculate the total volume of the tennis balls and then subtract that from the volume of the container.
-
Calculate the volume of one tennis ball: The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( r \) is the radius. Given that the radius of a tennis ball is 2.5 inches and using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (2.5)^3 \]
First, calculate \( (2.5)^3 \):
\[ (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625 \]
Now substitute this value into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 15.625 \]
Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.1867 \]
Now multiply by 15.625:
\[ V = 4.1867 \times 15.625 \approx 65.338 \]
So, the volume of one tennis ball is approximately 65.338 cubic inches.
-
Calculate the total volume of a dozen tennis balls: Since there are 12 tennis balls:
\[ \text{Total Volume of 12 Tennis Balls} = 12 \times 65.338 \approx 784.056 \]
-
Calculate the empty space in the container: Given that the volume of the container is 3,200 cubic inches:
\[ \text{Empty Space} = \text{Volume of Container} - \text{Total Volume of Tennis Balls} \]
\[ \text{Empty Space} = 3200 - 784.056 \approx 2415.944 \]
-
Round to the nearest whole number: The empty space, rounded to the nearest whole number, is:
\[ \approx 2416 , \text{in}^3 \]
Thus, the amount of empty space in the container is 2416 cubic inches.
1 answer