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A soccer ball with a diameter of 8.6 inches is shipped in a box that is a square prism and has a side length of 9.5 inches.

How much volume is available to be filled with packing material if the shipping company wants the box completely full? Round your answer to the nearest tenth

A soccer ball with a diameter of 8.6 inches is shipped in a box that is a square prism-example-1
User Keyur Shah
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1 Answer

3 votes

Answer:

Explanation:

To find the volume available for packing material, we need to calculate the volume of the box and subtract the volume of the soccer ball.

The volume of a square prism (box) is given by multiplying the area of the base (side length squared) by the height (which is also the side length in this case).

Volume of the box = (side length)^2 * side length = 9.5 inches * 9.5 inches * 9.5 inches

The volume of a sphere (soccer ball) is given by the formula (4/3) * π * (radius)^3. Since we have the diameter of the ball, we need to divide it by 2 to get the radius.

Radius of the soccer ball = 8.6 inches / 2 = 4.3 inches

Volume of the soccer ball = (4/3) * π * (4.3 inches)^3

Now, we can calculate the volume available for packing material:

Volume available for packing material = Volume of the box - Volume of the soccer ball

Make sure to use consistent units (in this case, cubic inches) throughout the calculation.

Once you have the numerical values, perform the calculations and round your final answer to the nearest tenth.

User Enbr
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