A box is filled with 6 cans of tennis balls. If the empty space was filled with sand, how much sand will be needed to fill the box?
Each can of tennis balls has a radius of 2 in.
Height of box is 12in.
More information needed. How big is the base of the box?
Packed in a single row of 6 cans or a double row of 3 cane each row, 1 x 6 or 2 x 3, the box volume is the same; 4x24x12 = 1152 cub.in. or 8x12x12 = 1152 cub.in.
The volume of the cans is 3.14(2)^2(12)6 = 904.778 cub.in.
THe sand is therefore the difference.
To calculate the amount of sand needed to fill the box, you'll first need to find the volume of the empty space in the box. Here's how you can do that:
1. Find the volume of each can of tennis balls: The volume of a cylinder (which a can of tennis balls resembles) can be calculated using the formula V = π * r^2 * h. Since the radius of each can of tennis balls is given as 2 inches and the height is not given, we'll assume a height of 4 inches for each can. Thus, the volume of each can is V = π * (2^2) * 4.
2. Determine the total volume of the cans: Since there are 6 cans of tennis balls, you can multiply the volume of each can by 6 to find the total volume of the cans.
3. Calculate the volume of the box: The volume of the box can be obtained by multiplying the length, width, and height of the box. However, since the length and width are not provided, we'll assume a length and width of 6 inches each (to accommodate the cans). Thus, the volume of the box is V = 6 * 6 * 12.
4. Calculate the empty space: Subtract the total volume of the cans (calculated in step 2) from the volume of the box (calculated in step 3). This will give you the volume of the empty space in the box.
Now that we have the volume of the empty space, we can calculate the amount of sand needed by converting the volume to a weight measurement (such as pounds or kilograms) based on the density of the sand. The density of sand can vary, so you'll need to consult a reliable source or measure it using a scale.