SOLUTION: A sphere has a volume of 32 in. If the diameter is halved, find the new volume. help..!!!

Question 420807: A sphere has a volume of 32 in. If the diameter is halved, find the new volume. help..!!!

Found 3 solutions by richard1234, stanbon, ilana:
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
The diameter is half the original, so the volume is one eighth of the original volume (this is because the volume is proportional to the cube of the radius). The new volume is therefore (1/8)*32, or 4 in^3.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A sphere has a volume of 32 in^3. If the diameter is halved, find the new volume.
----
Vol = (4/3)pi*r^3
---
32 = (4/3)pi*r^3
24 = pi*r^3
---
r = (24/pi)^(1/3)
------
If the diameter is halved, the radius is halved
---
New radius = (1/2)(24/pi)^(1/3)
New radius = (1/8)^(1/3)*(24/pi)^(1/3)
New radius = (3/pi)^(1/3)
---
New volume = (4/3)pi^3
---
New volume = 4 cu in.
=======================
Cheers,
Stan H.
=======================
Answer by ilana(307)   (Show Source): You can put this solution on YOUR website!
The volume of a sphere is 4/3*pi*r^3. So in this case 4/3*pi*r^3=32, so pi*r^3=32*3/4=24. So r^3=24/pi, so r is the cubed root of 24/pi, or (24/pi)^1/3 inches. Note that this is about 2 inches. The diameter is halved, so the radius is as well, so the radius is now ((24/pi)^1/3)/2. Now plug this back into the formula. 4/3*pi*r^3= (4/3)*pi*(24/8pi)= 4 cubic inches.
Note that you can figure this out from just the formula. V=(4/3)*pi*r^3, so when you plug in "r/2" for r, the volume will be V/2^3, which is V/8, or 4 cubic inches.
RELATED QUESTIONS
A sphere has a volume of 457 4/3 pi m3. the radius is halved. What is the new radius and... (answered by Alan3354)
The volume of a sphere is 32π in�. If the radius is doubled, what is the new... (answered by Fombitz)
If the radius of a sphere is halved, how is the volume and surface area... (answered by Alan3354)
if a sphere has a diameter of 30 what is half the volume of the... (answered by Alan3354)
a sphere has a diameter of 4 cm. what is the volume of the... (answered by edjones)
A sphere has a volume of 25m^3. What is the diameter in... (answered by stanbon)
The diameter of a sphere is 6 ft. Find the exact volume of the... (answered by Cromlix,MathTherapy)
Find the diameter of a sphere to the nearest 100th if its volume is 660mm cubed (answered by stanbon)
Find the volume of a sphere with diameter 21... (answered by lynnlo,Alan3354)