Volume of a Sphere?

Question

What is the exact volume of a sphere with a diameter of 4cm?

I know what the answer is 256¶ over 3,
but I don't know how to get it.
I've tried;
4¶(8)³ over 3, but I didn't get the answer.
anyone know what I'm doing wrong or how to get it?

thanks everyone. sorry if I was confusing.

Answer 1

1) I don't know what you're attempting to represent with the paragraph symbol, but I'm going to guess that you're using it to indicate π ("pi"). However, your assumed answer can't possibly be correct if the diameter is 4:

Remember to use the appropriate units; when the linear dimensions are expressed in cm, the volume is calculated in cm³ (also known as "cc").

In the following:

cm = centimeter or centimeters
D = diameter
r = radius
r³ = the cube of the radius
s¹ refers to the subject sphere,
V = volume

2a) Since the volume of a sphere is r³ 4 π / 3, and
2b) Since (based on the assumption indicated in (1) you expressed the volume as 256 π / 3,
2c) 4 r³ = 256
2d) r³ = (256 / 4) = 64.

3) Since the cube root of 64 is 4, rs¹ = 4

4a) Checking our work, when Ds¹ = 8;
4b) rs¹ = (8 / 2) = 4;
4c) r³ = (4 x 4 x 4) = 64
4d) 4 r³ = (4 x 64) = 256
4e) Vs¹ = 256 π / 3

That should obviously be close enough to reasonably prove the precedent assumptions.

5a) If, as you first assert, Ds¹ = 4;
5b) rs¹ = (2 / 2) = 2;
5c) r³ = (2 x 2 x 2) = 8
5d) 4 r³ = (4 x 8) = 32
5e) Vs¹ = 32 π / 3

6a) We've proved that for rs¹ = 4 cm, Vs¹ = 256 π / 3 cm³; and
6b) we've proved that for Ds¹ = 4 cm, Vs¹ = 32 π / 3 cm³.

7a) Since 256 / 32 = 8, and
7b) Since there isn't a common unit that is equal to 1/8 cm³,
7c) It does not appear that the figure 256 π / 3 can be ascribed to Vs¹.
7d) If you're relying on published answers to a textbook problem, you've obviously either uncovered a misprint or misread the problem.

.

Answer 2

The formula you need is four thirds pi times the radius cubed.

The radius is half the diameter, so you start by cubing 2(cm) to get 8(cm^3).

now multiply this 8 by pi

8 times 3.142 = 25.136 (cm^3)

now multiply this ans by 4/3

This will give an answer between about 33 and 34 cm^3

Remember the radius is half the diameter - everything else you did was right.

I don't know who told you the answer was 256 pi over 3. It can't possibly be - that is over a quarter of a litre.

The ball has a diameter of less than 2 inches - it cannot occupy 1/4 of a litre

Answer 3

given diameter of a sphere is 4 cm
formula for volume of sphere is 4/3 pi r^3
since diameter is given convert it into radius r=d/2
r=4/2
=2 cm
volume of shpere is 4/3x22/7x2x2x2
=88/21x8= 704/21 cm cube

Answer 4

The volume is 4/3*pi*r^3

Hmmm...are you sure you looked up the right answer because based on your information the answer should be 32*pi over 3?

Answer 5

4/3 Pi r*3

4 * pi * 4^3 / 3

256 Pi /3

Answer 6

4/3 pi*r^3

Answer 7

it is 4/3 TTr3.

Answer 8

The way to solve this is to integrate in three dimensions.
Use the method of disks.