Question

the side of the cube is equal to the diameter of the sphere . find the ratio of their volumes​

Answer 1

Answer:

Step-by-step explanation:

The ratio of volume of sphere to volume of cube is " : 1". Hence, the ratio of volume of sphere to volume of cube is [tex]\dfrac{\pi }{6} : 1

Answer 2

Answer:

The ratio of volume of sphere to volume of cube is "\dfrac{\pi }{6}

6

π

: 1".

Step-by-step explanation:

Let diameter of the sphere = d = side of the cube

∴ Radius of the sphere(r) = \dfrac{d}{2}

2

d

Volume of sphere =\dfrac{4}{3}\pi\[r^{3}

3

4

π\[r

3

=\dfrac{4}{3}\pi\dfrac{d}{2}r^{3}

3

4

π

2

d

r

3

= \dfrac{\pi }{6}d^{3}

6

π

d

3

And,

Volume of the cube = d^{3}d

3

∴ The ratio of volume of sphere to volume of cube

= \dfrac{\pi }{6}

6

π

d^{3}d

3

: d^{3}d

3

= [tex]\dfrac{\pi }{6} : 1

Hence, the ratio of volume of sphere to volume of cube is [tex]\dfrac{\pi }{6} : 1.

Step-by-step explanation:

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