Question

the surface area of a sphere is 324π
square cm find its volume how many smaller spheres of diameter 1 cm can be made out of it

Answer 1

Answer:

Surface area of sphere=324πcm²

=4πr²=324π

= r²=324/4

=r=√81

=r=9cm

Volume of sphere = (4/3)πr³

=(4/3)×π×9³

Diameter of smaller sphere=1cm

Radius of smaller sphere= 0.5cm

Volume of smaller sphere=(4/3)×π×(0.5)³

No. of smaller spheres :

Volume of Sphere

=-----------------------------------------

Volume of smaller sphere

(4/3)π×9³

=---------------------------------

( 4/3)π(0.5)³

=9³/(0.5)³

=729/0.125

=5832

Thus, 5832 smaller spheres can be made.

Correct me if I'm wrong.

Answer 2

Number of Smaller Sphere = 5832

Step-by-step explanation:

It is given that,Surface Area=324π

We know that, $Surface\ area\ of\ sphere=4\pi r^2$

                       $324\pi= 4\pi r^2$                

                        $r^2=324\pi /4\pi$

                        $r^2=81$

                        r= 9 cm

   Diameter of smaller sphere = 1 cm

  $Radius\ of\smaller\ sphere = 1/2 \times diameter$

                                             $= 1/2 \times 1 cm$

                                               = 0.5 cm

    Now, Volume of sphere with large diameter = Volume of sphere of smaller diameter × Number of sphere

   $4/3 \times \pi r_1^3 = 4/3 \times \pi r_2^3 \times Number\ of\ smaller\ sphere$

   $4/3 \times \pi (9)^3 = 4/3 \times \pi (0.5)^3 \times Number\ of\ smaller\  Sphere$

 Number of Sphere= $\frac{4/3 \times  \pi (9)^3}{4/3 \times \pi (0.5)^3}$

$Number of Sphere= \frac {9\times 9\times 9}{0.5\times 0.5\times 0.5}$

Number of  Smaller Sphere=729000/125

                              =5832