Question

HELP PLEASE!!
Which is greater, the total volume of three spheres, each of which has a diameter 3 in., the volume of one sphere that has a diameter 8 in., or the volume of a hemisphere with a diameter of 9 in.?
a) The volume of three spheres, each with a diameter of 3 inches, is greater.
b) The volume of one sphere with a diameter of 8 inches is greater.
c) The volume of the hemisphere with a diameter of 9 in. is greater.
d) The two volumes are the same.

Answer 1

The answer is c

Answer 2

really?

Answer 3

1) Volume of Sphere is 4/3 * pi * r^3

If the diameter is 3, then the radius is 3/2

V = 4/3 * pi * (3/2)^3

V = 9*pi/2

Three of these spheres would have a volume of 3 * (9*pi/2) = 27*pi / 2

Answer 4

the volume of one sphere that has a diameter 8 in.

V = 4/3 * pi * 4^3 where the radius is 4.

V = 256* pi /3

Answer 5

can you help with another?

Answer 6

the volume of a hemisphere with a diameter of 9 in.

Volume of hemisphere = 1/2 that of the sphere

V = 1/2 * 4/3 * pi * (9/2)^3

V = 343*pi/4

Answer 7

@dengeki_daisy Of these three volumes, which option is correct?

Answer 8

>The answer is c

@Divyankasc

I don't agree. Please show your work.

Reminder: Direct Answers are against the OpenStudy rules.

Answer 9

@Directrix
I'm not really sure how to figure it out, can you explain it differently

Answer 10

No, I explained it the only way I know how.

Learn the formula for the volume of a sphere and use it to compare volumes.

Answer 11

okay I will

Answer 12

It comes down to which of these is the largest:

27*pi/2 or 256*pi/3 or 343* pi/4

Answer 13

ohh well then, C

Answer 14

@Directrix

Answer 15

Option C is the hemisphere and has volume V = 343*pi/4 .That approximates to 269.39.

Is that larger than the approximation for the other two volumes?