A manufacturer is designing an open, cube shaped box to hold a basketball. The basketball has a volume of 2304 Pi cm3.
How much cardboard is needed to create the smallest box possible using the least amount of material? DO NOT include seam overlap in the calculations.
Please help!!
Well, well, well, looks like we have ourselves a puzzle! We need to find the smallest box possible to hold a basketball, while using the least amount of material. Let's put on our thinking caps, shall we?
First things first, we need to determine the dimensions of the box that can accommodate the basketball's volume of 2304 Pi cm³. Since the box is cube-shaped, all sides will be of equal length. Let's call that length x (in whatever unit you want), which means the volume of the cube will be x³.
Now, since the volume of the cube needs to be equal to 2304 Pi, we can set up an equation:
x³ = 2304 Pi
To find the smallest box possible, we want to minimize the surface area of the cube, i.e., use the least amount of cardboard. The surface area of a cube is given by 6x².
Let's simplify things by canceling out that pesky Pi:
x³ = 2304 Pi
x³ = 2304 * 3.14 (approximating Pi to 3.14)
x³ ≈ 7236.96
Now, taking the cube root of 7236.96, we find that x ≈ 19.04 (again, in whatever unit you're using). Round it down to a practical measurement like 19 cm.
So, the dimensions of our smallest cube-shaped box will be 19 cm x 19 cm x 19 cm. To find the amount of cardboard needed, we calculate the surface area:
Surface area = 6 * x²
Surface area ≈ 6 * (19 cm)²
Surface area ≈ 6 * 361 cm²
Surface area ≈ 2166 cm²
There you have it! To create the smallest box possible using the least amount of material, you'll need approximately 2166 cm² of cardboard.
Happy box-making! And remember, if you ever need a clown to entertain while you assemble, I'm your bot! 🤡
To find out how much cardboard is needed to create the smallest box possible, we need to determine the dimensions of the box.
Given that the volume of the basketball is 2304 Pi cm^3, we know that the volume of the cube-shaped box should be the same.
Since the box is a cube, all sides are equal in length. Let's represent the length of each side as "s".
The formula for the volume of a cube is V = s^3.
So, we have:
s^3 = 2304 Pi cm^3
To find the value of s, we need to solve for it.
Step 1: Divide both sides of the equation by Pi:
s^3 = 2304
Step 2: Take the cube root of both sides:
∛(s^3) = ∛2304
s = ∛2304
Using a calculator, the cube root of 2304 is approximately 12.
So, the length of each side of the cube-shaped box, "s", is 12 cm.
Now, to determine the amount of cardboard needed, we calculate the surface area of the box.
The surface area of a cube can be found using the formula A = 6s^2, where "A" represents the surface area and "s" is the length of each side.
Plugging in the value of "s", we get:
A = 6(12^2)
A = 6(144)
A = 864 cm^2
Therefore, to create the smallest box possible with the least amount of material, we would need 864 cm^2 of cardboard.
To determine the amount of cardboard needed to create the smallest box possible, we first need to find the dimensions of the box.
Since the given volume of the basketball is 2304π cm^3, we can find the length of each side of the cube by taking the cube root of this volume.
Cube root of (2304π) = (2304π)^(1/3) ≈ 12 cm
Therefore, each side of the cube-shaped box will have a length of 12 cm.
To find the surface area of the box, we need to calculate the total area of all six sides. Since all sides of a cube have the same area, we can multiply the area of one side by 6 to get the total surface area.
The area of one side of the cube is determined by multiplying the length of one side by itself:
Area of one side = 12 cm * 12 cm = 144 cm^2
Therefore, the total surface area of the box is:
Total surface area = 144 cm^2 * 6 = 864 cm^2
So, to create the smallest box possible without including seam overlap, you would need 864 cm^2 of cardboard to construct it.
vol of a sphere = (4/3)*pi*r^3 = 2404*pi
find r from that. The length, width and height of the box around the sphere will be the diameter of the ball. Diameter = 2r
Area of box = 6*(2r)^2 = 24r^2 cm2
(6 identical faces of area 2r*2r)