Answer:
A.) 1018 square inches
Step-by-step explanation:
The largest sphere will have a diameter equaling the length of the cube (see picture).
If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:
![SA=4\pi r^2](https://tex.z-dn.net/?f=SA%3D4%5Cpi%20r%5E2)
For this formula, we need the radius of the sphere. Divide the diameter by 2:
![\frac{18}{2}=9](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B2%7D%3D9)
The radius is 9 inches. Plug this into the equation:
![SA=4\pi *9^2](https://tex.z-dn.net/?f=SA%3D4%5Cpi%20%2A9%5E2)
Simplify the equation:
![SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87](https://tex.z-dn.net/?f=SA%3D4%5Cpi%20%2A81%5C%5C%5C%5CSA%3D324%5Cpi%20%5C%5C%5C%5CSA%3D1017.87)
Round the result to the nearest whole number:
→
The surface area is 1,018 inches².
:Done
Picture:
In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.
Answer:
7) A school group is assigned to survey vast museum collections of all macroscopic (not microscopic) animal species collected from various regions around the world. What observation are the students most likely to make? A) The majority of the animals are wormlike. B) The majority of the animals possess a …
Step-by-step explanation:
Answer:
d = 69°, e = 32°, f = 79°
Step-by-step explanation:
the 69° angle and d are vertical angles, so d is 69°.
same with e and the 32° angle, so e is 32°.
the 69° angle and f are on a straight angle, which means they, and e, add up to 180° when combined.
69 + 32 = 101
180 - 101 = 79
so f is 79°.
We can see that
lies just before 0,
lies between 2 and 3m and
lies between 4 and 5. So, we have
![-1 < a < 0,\quad 2 < b < 3,\quad 4 < c < 5](https://tex.z-dn.net/?f=%20-1%20%3C%20a%20%3C%200%2C%5Cquad%202%20%3C%20b%20%3C%203%2C%5Cquad%204%20%3C%20c%20%3C%205%20)
In particular, this implies that
![-1+4 < a+c < 0+5 \iff 3 < a+c < 5](https://tex.z-dn.net/?f=%20-1%2B4%20%3C%20a%2Bc%20%3C%200%2B5%20%5Ciff%203%20%3C%20a%2Bc%20%3C%205%20)
So, the correct order would be
![-2,\ b,\ a+c](https://tex.z-dn.net/?f=%20-2%2C%5C%20b%2C%5C%20a%2Bc%20)
Answer:
y=1/x -9
Step-by-step explanation: