Question

if 1000 spherical of radius 1 cm are melted to form a bigger bulb. Then find the radius of bigger bulb​

Answer 1

Answer:

10 cm

Step-by-step explanation:

Given:

No. of small spherical bulb = 1,000

radius (r) of smaller bulbs = 1 cm

Required:

radius of the bigger bulb

SOLUTION:

The following equation represents the relationship of the volume of the smaller and bigger bulb,

$\frac{V_2}{V_1} = 1,000$

Where,

$V_2$ = volume of bigger bulb

$V_1$ = volume of smaller bulb

1,000 is the number of smaller bulbs melted to form the bigger bulb.

Volume of a sphere is given as, ⁴/3πr³

Therefore:

$V_2$ = ⁴/3*π*r³ = 4πr³/3

$V_1$ = ⁴/3*πr³ = ⁴/3*π*(1)³ = ⁴/3π*1 = 4π/3

Plug the above values into the equation below:

$\frac{V_2}{V_1} = 1,000$

$\frac{\frac{4*pie*r^3}{3}}{\frac{4*pie}{3}} = 1,000$

$\frac{4*pie*r^3}{3}*{\frac{3}{4*pie} = 1,000$

$\frac{4*pie*r^3*3}{3*4*pie} = 1,000$

$\frac{12*pie*r^3}{12*pie} = 1,000$

$r^3 = 1,000$ (12pie cancels 12 pie)

$r = 10$ (taking the cube root of each side)

Radius of the bigger bulb = 10 cm