Volume Math Question?

Question

I have tried to solve this many times but I can't

Q: A store sells two chocolate baseballs for the same price. One is hollow sphere 10 cm in diameter on the outside, with a shell that is 1 cm thick. The other is a solid sphere with a diameter 8 cm. Which sphere contains more chocolate?

What I did:

I treated the diameter on the outside as the diameter of the sphere. So for the hollow sphere, I found the volume of the entire sphere, then using 10cm-2cm= 8cm as the diameter for the inner hollow part to calculate that part of volume. Then I substract the total volume of the hollow sphere by the volume of the inner hollow part, therefore I can get the volume of the solid thickness of chocolate of the hollow sphere.

Next in terms of the solid sphere, I just use the simple formula, plug in the radius (4cm) and calculate the volume.

In the end my answer was that the solid sphere contains more chocolate than the hollow but the answer was suppose to be the HOLLOW SPHERE.

Please help

Answer 1

Based on the info you have provided, you seem to be correct.

The volume of the first baseball is:

V = (4/3)(pi)(5)^3 - (4/3)(pi)(4)^3) = (244/3)(pi) cm^3

* That is the volume of a solid 10 cm diameter baseball minus the volume of the hollow portion.

The volume of the solid baseball is:

V = (4/3)(pi)(4)^3 = (256/3)(pi) cm^3

Either the answer you were provided is wrong, or some of the info you've written is incorrect.

Answer 2

The hollow sphere has a volume of 4/3*pi *5^3 - 4/3* pi*4^3
= 4pi/3(5^3-4^3) = 4pi/3 * 61 = 255.52 cm^3

The volume of the solid sphere is 4pi/3*4^3 = 268.08 cm^3

The 8" diameter solid ball contains more chocolate that hollow 10" ball with a 1" shell.

You are right. The rest of the world is wrong.

Answer 3

Your mistake was the RADII of outer and inner spheres in the hollow chocolate. The outer radius is 5 cm, while the inner radius (the empty part) has radius 4. So the hollow sphere's chocolate volume is 4/3π(5)³ - 4/3π(4)³ = 244π/3 cm³

The solid sphere has radius 4, so its total volume is simply 4/3 π*4³ = 256π/3 cm³. The solid is bigger by 4π cm³!!

Answer 4

Volume of a sphere

volume=4/3¶r3

Hollow Sphere

Large sphere = 4/3 (pi)(5)^3=523 cubic cm

Inner sphere = 4/3 (pi)(4)^3=268 cubic cm

Total sphere = 523 – 268 = 255 cubic cm

Solid sphere

Inner sphere = 4/3 (pi)(4)^3=268 cubic cm

The volume of the solid sphere is greater as you calculated. I also ran the objects through AUTOCAD in 3D and had the same exact answers.

Answer 5

The ratio of the horrow sphere to the solid sphere equals to
(4pi/3)(5^3-4^3)/[(4pi/3)4^3]
= 63/64

Therefore, the solid sphere contains more chocolate.

Answer 6

V(hollow) = (4π/3) (Ro^3 - Ri^3)
V(hollow) / V(solid) = (Ro^3 - Ri^3) / Rs^3
(The constant cancels out if you divide.)
(5^3 - 4^3 / 4^3 = (5/4)^3 - 1 = 1.953125 - 1 = 0.953125
It looks to me like the solid sphere contains more chocolate. You might want to recheck the statement of the problem.

Answer 7

Volume of a sphere is.
V = 4/3(pi)(r^3)

For the solid sphere
V=(4/3)(3.14)(4^3)=(12.56/3)(64)=803.84/3=267.95 cubic centimeters
For the hollow sphere
If it were solid
V=(4/3)(3.14)(5^3)=(12.56/3)(125)=1570/3=(523.3333) cubic centimeters
The volume of the “empty” part is, but wait, since 5-1=4, we already did that!
So the actual volume of the chocolate in the hollow sphere is
(523.33)-(267.95)=255.38 cubic centimeters
To check myself I went to
http://grapevine.abe.msstate.edu/~fto/tools/vol/sphere.html
So I get the same answer, maybe misprint?

Answer 8

Using the formula for the volume of a sphere:

(4/3)(pi)r^3 and 3.14 for pi we have 4.19r^3
The value of (4/3)pi cancels out so it really doesn't make any difference for this question the accuracy of pi you choose.

So for the 1 cm shell its volume is:

(4.19)5^3-(4.19)4^3=
(4.19)(5^3-4^3)=255.59

The volume of the solid 8 cm is:

(4.19)4^3=268.16

So I agree with you. Check your problem again and if the starting values are right ask your teach to explain it.

Answer 9

What you did is exactly what you needed to do so let's check your calculations:

V=4pi*r^3
V of solid= 4pi*4^3 = 256 pi
V of hollow= 4pi 5^3 - 4.5pi 9^3 = 500pi- 364.5 pi =135.5 pi

You seem to have done it correct. I don't know what to tell you.

Answer 10

Lateral Surface Area = Perimeter of Base * height Total Surface Area = Perimeter of Base * height + 2(area of base) Volume = Area of Base * height Area (2D figure) is different for different figures