Suppose a ball has a diameter of 8.65 inches. What is the approximate volume of the ball? Round your answer to the nearest cubic inch.
V=(4/3)πr^3
V = (4/3) * 3.14 * 80.902
V = ______ cubic inches
2120
To find the approximate volume of the ball, we can use the formula for the volume of a sphere: V = (4/3)πr³, where V represents the volume and r represents the radius of the sphere.
In this case, we are given the diameter of the ball, which is 8.65 inches. To find the radius, we divide the diameter by 2: r = 8.65 / 2 = 4.325 inches.
Now that we have the radius, we can substitute it into the volume formula: V = (4/3)π(4.325³).
To calculate this, we need to know the value of π. π (pi) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is commonly approximated to 3.14.
Using the value of π = 3.14, we can calculate the volume:
V ≈ (4/3) * 3.14 * (4.325³)
V ≈ (4/3) * 3.14 * 81.793771875
V ≈ 343.193874167 cubic inches
Since rounding is required to the nearest cubic inch, we round the result to one decimal place:
V ≈ 343 cubic inches
Therefore, the approximate volume of the ball is 343 cubic inches.