A small shipping crate is a cube with a side length of 8 inches and a surface area of 384 square inches. A large shipping crate has a surface area of 864 square inches.
What is the side length of the large crate?
area = 4 pi r^2
volume = 4/3 pi r^3
So, for any sphere, the area:volume ratio is 3/r
However, I suspect that you garbled the question. Since area varies as the square of the diameter, if the diameters are in the ratio 3/4,
area is in the ratio (3/4)^2
volume is in the ratio (3/4)^3
no that's how the question is asked
where did the cylinder come from?
Area grows as the square of the scale. So,
864/384 = s^2/8^2
s = 12
To find the side length of the large crate, we can set up a proportion using the surface area of the small crate and the surface area of the large crate.
Let's call the side length of the large crate "x".
We can set up the proportion as follows:
(384 square inches) / (8 inches)^2 = (864 square inches) / (x inches)^2
To solve for x, we can cross multiply:
384 * (x inches)^2 = 864 * (8 inches)^2
Now, we can divide both sides of the equation by 384 to isolate (x inches)^2:
(x inches)^2 = (864 * (8 inches)^2) / 384
Next, we can simplify the equation:
(x inches)^2 = 18 * (8 inches)^2
Now, we can take the square root of both sides to solve for x:
x inches = √(18 * (8 inches)^2)
x inches = √(18) * 8 inches
Finally, we can calculate the value of x:
x inches ≈ 12.85 inches
Therefore, the side length of the large crate is approximately 12.85 inches.