Question

(16) If a solid sphere of radius 10 cm is moulded into 8 spherical balls of
equal radii, what is the surface area of each ball ?
b. 752
c. 607
d. 504
a. 100

​

Answer 1

100π cm²

Step-by-step explanation:

Given:

Solid Sphere of radius 10 cm is moulded into 8 spherical balls.

To find:

Surface Area of each sphere

Point to be Noted:

1. As the object is moulded we have to find volume.

2. Volume of each object will remain unchanged.

3. Formula will be Used.

4. Formation and solution of equation are required.

Solution:

Radius of sphere = 10 cm

Volume of sphere = 4/3 π (10)³ cm³

let, the radius of each sphere be r cm.

Volume = 4/3 π r³ cm³

According to question,

$8 \times \frac{4}{3}\pi{r}^{3} = \frac{4}{3} \pi {(10)}^{3} \\ \\8 \: \: \cancel{\frac{4}{3}} \:\cancel{\pi}{r}^{3} = \cancel{\frac{4}{3}} \: \cancel{\pi} \: {(10)}^{3} \\ \\ 8 {r}^{3} = {(10)}^{3} \\ \\ {(2r)}^{3} = {(10)}^{3}$

[Eliminating Cube From both side]

$2r = 10 \\ \\ \cancel{2}r = \cancel{10} \\ \\ r = 5 \: cm$

Hence, The radius of each sphere is 5 cm.

So, Surface Area = 4πr²

= 4 π (5)² cm²

= 4 × 25 π cm²

= 100π cm²

Therefore, the required Surface Area is 100π cm².

Formula Related to Sphere:

Volume = 4/3πr³ unit³

Surface Area = 4πr² unit²

[Here r is radius of any sphere]

Answer 2

$\huge \purple A \purple N \purple s\purple W \purple e \purple \R :-$

Volume of solid sphere = 4/3πR^3

= 4/3 × 22/7 × 10 × 10 × 10

= 88000/21 cm^3 .

∴ Volume of spherical ball = 88000/21 cm^3

Volume of 1 spherical ball = 11000/21 cm^3

=> 4/3πr^3 = 11000/21

=> r^3 = 11000 × 3 × 7 / 21 × 4 × 22 = 125

=> r = 3√125 = 5 cm .

∴ Surface area of each ball = 4πr^2

= 4 × 25 × π

= 100π

Option (a) is correct answer