Question

Find X in the image
if the volume of the
cylinder and the
sphere are equal ​

Answer 1

Answer:

Volume of the sphere =

3

4

πr

3

cylinder =$$

Volume of cylinder =πr

2

h=πr

2

.2r(as it is given radius of cylinder =r and h=2r)

Volume of Sphere=

3

2

πr

2

(2r)=

3

2

volume of cylinder

Answer 2

Answer:

The value of x is d/3.

Step-by-step explanation:

Volume of the cylinder = πr²h

Volume of the cylinder = π(d/2)²h ...(i)

Volume of the sphere = (4/3)πr³

Volume of the sphere = (4/3)π(d/2)³ ...(ii)

The height of the cylinder is equal to d-x.

It is given that the volume of the cylinder and the sphere are equal. Therefore, by equating equations (i) and (ii) and substituting h = d-x, we get

$\pi( \frac{d}{2})^{2} (d-x) = \frac{4}{3}\pi ( \frac{d}{2})^{3}$

$d-x = \frac{4}{3} (\frac{d}{2})$

$d-x = \frac{2d}{3}$

$x = d - \frac{2d}{3}$

$x = \frac{3d-2d}{3}$

x = d/3

Hence, the value of x is d/3.

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