172, since he bought two boxes and each had 516 there was 1,032 in all. Since he wants them to last 6 months, then you divide by six and get 172 :) I think this is what it is asking.
Pick’s Theorem is used to find the areas of figures on lattices easily. The formula is:
A = (B)/2 + I - 1, where B is the number of points on the border of the shape, and I is the number of points inside the shape.
Here, there are 8 points on the outside of the shape, and there are 12 points inside the shape. So, we do:
8/2 + 12 - 1 = 4 + 12 - 1 = 15 units squared.
We can check by finding the areas of the non-shaded region and subtracting that area from the whole rectangle area of 4 * 10 = 40:
4 * 1 + (3 * 1)/2 + 1 * 9 + (3 * 1)/2 + (9 * 2)/2 = 25
40 - 25 = 15, so we’re right!
The answer is 15 units squared, or choice (B).
First, solve for the radius of the sphere using the volume and the equation,
V = 4πr³ / 3
Substituting for the known values,
3000π m³ = 4πr³/3
The value of r from the equation is approximately 13.10 meters. The equation for the surface area is,
SA = 4πr²
Substituting the value of radius,
SA = 4π(13.10 m)² = 2157.74 m²
Therefore, the surface area is approximately 2157.74 m².
