Question

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

Answer 1

10 cm

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,

`(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:

`(V_2)/(V_1) = 1,000`

`((4*pie*r^3)/(3))/((4*pie)/(3)) = 1,000`

`(4*pie*r^3)/(3)*{(3)/(4*pie) = 1,000`

`(4*pie*r^3*3)/(3*4*pie) = 1,000`

`(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