To find the dimensions of the cube box that will snugly fit the spherical soap, we first need to determine the radius of the sphere.
The formula for the surface area \(A\) of a sphere is given by: \[ A = 4\pi r^2 \] where \(r\) is the radius of the sphere. We can rearrange this formula to solve for \(r\): \[ r^2 = \frac{A}{4\pi} \] \[ r = \sqrt{\frac{A}{4\pi}} \]
Given that the surface area \(A\) is 63.585 in² and using \(\pi \approx 3.14\), we can calculate \(r\).
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Calculate \(4\pi\): \[ 4\pi \approx 4 \times 3.14 = 12.56 \]
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Now calculate \(r^2\): \[ r^2 = \frac{63.585}{12.56} \approx 5.06 \]
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Calculate \(r\): \[ r = \sqrt{5.06} \approx 2.25 \text{ in.} \]
The diameter \(d\) of the sphere is: \[ d = 2r \approx 2 \times 2.25 = 4.5 \text{ in.} \]
Since the soap is spherical and we want a cube box that fits it snugly, the side length of the cube box should be equal to the diameter of the soap.
Therefore, the dimensions of the cube box should be: \[ 4.5 \text{ in.} \times 4.5 \text{ in.} \times 4.5 \text{ in.} \]
The correct response is: 4.5 in. × 4.5 in. × 4.5 in.