Help with maths question

Question

A spherical party ballon is blown up to help decorate a room. 

Find the volume of air, correct to 2d.p. Need for the ballon to be:

a)10cm wide 

b)20 cm wide 

c)30cm wide

2) if the ballon pops when the volume of air reaches 120000cmcube , find the diameter of the ballon at that point correct to 1 d.p.

Answer 1

(1)

 

(a) d = 10 cm

 

r = d/2 = 10/2 cm = 5 cm

 

V = (4/3) * pi * r^3 = (4/3) * pi * (5 cm)^3 = 523.60 cm^3

 

 

(b) d = 20 cm

r = d/2 = 20/2 cm = 10 cm

V = (4/3) * pi * r^3 = (4/3) * pi * (10 cm)^3 = 4188.79 cm^3

 

 

(c) d = 30 cm

r = d/2 = 30/2 cm = 15 cm

V = (4/3) * pi * r^3 = (4/3) * pi * (15 cm)^3 = 14137.17 cm^3

 

 

(2)

 

d = 2r = 2 * [(3/4) * V / pi]^(1/3) =  2 * [(3/4) * (120000 cm^3 / pi]^(1/3) = 61.20 cm