# Math Help - Finding total surface area of a sphere +more

1. ## Finding total surface area of a sphere +more

I have a sphere that is 1.5 inches in diameter thus it has a radius of .75 inches. I have found a formula that gives me the total surface area.

The formula I found is: $4x3.14x.75^2$

My problem is once I find the total surface area I need to find a way to fit atleast 30 diamonds into that total space. So according to the formula, the total space comes out to 7.065 inches. If this is the case, then I asume that would be a 7.065 by 7.065 flat area? If so how can I figure out how to fit 30 diamonds into that space? So far I have a diamond dimension of .75 inches wide and 2.25 inches long / tall. That comes out to around 27 diamonds.

40b1t

2. Originally Posted by 40b1t
I have a sphere that is 1.5 inches in diameter thus it has a radius of .75 inches. I have found a formula that gives me the total surface area.

The formula I found is: $4x3.14x.75^2$

My problem is once I find the total surface area I need to find a way to fit atleast 30 diamonds into that total space. So according to the formula, the total space comes out to 7.065 inches. If this is the case, then I asume that would be a 7.065 by 7.065 flat area? If so how can I figure out how to fit 30 diamonds into that space? So far I have a diamond dimension of .75 inches wide and 2.25 inches long / tall. That comes out to around 27 diamonds.

40b1t
1. The formula you use is correct:

$A_{surface\ of\ sphere}=4 \cdot \pi \cdot r^2$

With your value of r = 0.75'' you'll get $A_{surface\ of\ sphere}=4 \cdot \pi \cdot(0.75)^2\approx 7.0686\ square\ inches$

2. If you transform this area into a square then its side length would be:

$s=\sqrt{7.0686\ square\ inches} \approx 2.659\ inches$

3. Since one diamond is nearly as long as one side of this square you can't place more than 4 diamonds on this area.