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,
[tex] \frac{V_2}{V_1} = 1,000 [/tex]
Where,
[tex] V_2 [/tex] = volume of bigger bulb
[tex] V_1 [/tex] = 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:
[tex] V_2 [/tex] = ⁴/3*π*r³ = 4πr³/3
[tex] V_1 [/tex] = ⁴/3*πr³ = ⁴/3*π*(1)³ = ⁴/3π*1 = 4π/3
Plug the above values into the equation below:
[tex] \frac{V_2}{V_1} = 1,000 [/tex]
[tex] \frac{\frac{4*pie*r^3}{3}}{\frac{4*pie}{3}} = 1,000 [/tex]
[tex] \frac{4*pie*r^3}{3}*{\frac{3}{4*pie} = 1,000 [/tex]
[tex] \frac{4*pie*r^3*3}{3*4*pie} = 1,000 [/tex]
[tex] \frac{12*pie*r^3}{12*pie} = 1,000 [/tex]
[tex] r^3 = 1,000 [/tex] (12pie cancels 12 pie)
[tex] r = 10 [/tex] (taking the cube root of each side)
Radius of the bigger bulb = 10 cm
