Consider this sphere with a diameter of 5 m.
What can be concluded about the sphere? Check all
that apply,
The sphere has a radius of 10 cm.
The diameter measure is substituted into the
formula to find the volume.
5 m
The radius is half the diameter.
The formula to apply is y=- Bh
The volume of the sphere is two-thirds the volume
of a cylinder with the same radius and height.

9514 1404 393

Step-by-step explanation:

Regardless of the diameter, the radius is half the diameter. For this sphere, it is 5/2 m = 2.5 m.

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The height of the sphere is equal to its diameter, so is 2r. The volume of a cylinder with radius r and height 2r is ...

  V = πr²h = πr²(2r) = 2πr³

The volume of a sphere with radius r is ...

  V = 4/3πr³

Then the ratio of sphere volume to cylinder volume is ...

  (4/3πr³)/(2πr³) = (4/3)/2 = 2/3

The sphere volume is 2/3 that of a cylinder with the same radius and height.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation