Question:-Six spherical cannon balls are tightly packed into a rectangular box in one layer. Each row has two cannon balls and each column has three. What part of the box is empty?Choices:- 15/21 14/21 10/21 14/23

To solve this problem, we need to understand how spheres (cannon balls) pack in a rectangular box.

Step 1: Calculate the volume of the box The box has 2 balls in each row and 3 balls in each column. If we assume the radius of each ball is r, then the length of the box is 22r = 4r (two diameters) and the width of the box is 32r = 6r (three diameters). Since the balls are packed in one layer, the height of the box is 2r (one diameter). So, the volume of the box is lengthwidthheight = 4r6r2r = 48r^3.

Step 2: Calculate the total volume of the balls The volume of a sphere (ball) is given by the formula 4/3πr^3. Since there are 6 balls, the total volume of the balls is 64/3π*r^3 = 8πr^3.

Step 3: Calculate the part of the box that is empty The part of the box that is empty is 1 - (total volume of the balls / volume of the box) = 1 - (8πr^3 / 48r^3) = 1 - π/6.

Step 4: Convert the fraction to have a denominator of 21 (to match the answer choices) Multiplying the numerator and denominator by 7 gives 7 - 7π/42.

Looking at the answer choices, none of them match this result. There seems to be a mistake in the answer choices. The correct answer should be 7 - 7π/42.