se the formula for the volume of a sphere to solve the following problem.
How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth.
(1 point)
Responses
3,052.1 in.3
3,052.1 inches cubed
190.8 in.3
190.8 inches cubed
113 in.3
113 inches cubed
381.5 in.3
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
In this problem, we are given the diameter of the basketball, which is 9 inches. The radius is half the diameter, so the radius is 4.5 inches.
Substituting the radius into the formula, we have V = (4/3)π(4.5)^3.
Calculating this expression, we find V ≈ 381.5 in.3.
Therefore, the answer is 381.5 in.3.
The volume of a container measures 4,000 mm3 and contains 50 marbles. Each marble has a radius of 2 mm. Use 3.14 as an approximation for pi. How much space in the box is unused? Round your answer to the nearest tenth.(1 point)
Responses
2,325.3 mm3
2,325.3 mm cubed
33.5 mm3
33.5 mm cubed
1,674.7 mm3
1,674.7 mm cubed
3,900 mm3
The volume of the container is given as 4,000 mm3.
To find the total volume occupied by the marbles, we need to calculate the volume of each marble and then multiply it by the total number of marbles.
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
In this problem, we are given the radius of each marble as 2 mm.
Substituting the radius into the formula, we have V = (4/3)π(2)^3.
Calculating this expression, we find V ≈ 33.5 mm3 for the volume of each marble.
To find the total volume of the marbles, we multiply this value by the total number of marbles, which is 50.
Total volume of the marbles = 33.5 mm3 * 50 = 1,675 mm3.
To find the space unused in the box, subtract the total volume of the marbles from the volume of the container:
Unused space = 4,000 mm3 - 1,675 mm3 = 2,325 mm3.
Therefore, the answer is 2,325.3 mm3.
To solve the problem, we need to use the formula for the volume of a sphere. The formula is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
First, we need to find the radius of the basketball. Since the diameter is given as 9 inches, the radius is half of the diameter, which is 9/2 = 4.5 inches.
Next, we substitute the value of the radius into the volume formula:
V = (4/3) * 3.14 * (4.5)^3
Calculating this expression, we get:
V = (4/3) * 3.14 * (91.125)
V ≈ 381.5 in.³
So, the answer is approximately 381.5 in.³, rounded to the nearest tenth.