Question

the diameter of a sphere is decreased by 25%.find it's new volume

Answer 1

Answer:

$27 \div 64$

Answer 2

Answer:

Step-by-step explanation:

Let the radius of the sphere be r

Therefore diameter = 2r

As we know that the volume of the sphere =  $\frac{4}{3}$ * π * r³

Now the diameter is decreased by 25%

=> Decrease = 25% of 2r

                     = $\frac{25}{100}$ * 2r

                     = r/2

Therefore, new diameter = Original diameter - Decrease

                                          = 2r - r/2

                                          = 3r/2

Therefore, new radius = 3r/4          (as radius = diameter/2)

Therefore, new volume = $\frac{4}{3}$ * π * (3r/4)³

                                        = $\frac{9}{16}$ * π * r³

The new volume is $\frac{9}{16}$ * π * r³ units³

Also,$\frac{original}{new}$ =  $\frac{\frac{4}{3} * \pi * r^{3}}{\frac{4}{3} * \pi *(\frac{3}{4}* r)^{3}}$ = $\frac{64}{27}$

Thus, we can also say that the new volume is $\frac{27}{64}$ times the original volume.