The total volume of two spheres is 10π cubic units. the ratio of the

areas is 4: 9. what is the volume of the smaller sphere in cubic units?

4 r1 ² π : 4 r2² π = 4 : 9
r1² : r2² = 4 : 9
r1 : r2 = 2 : 3
r2 = 3 r1/2   ( r - radius of the smaller sphere )
10 π = 4/3 r³ π + 4/3 ( 3 r/2 ) ³ π    /  : π/3
30 = 4 r³  + 4 * 27 r³/8
30 = 4 r³ + 27 r³/2    / * 2
60 = 35 r³
r³ = 60 / 35 = 12/7
V ( Smaller ) = 4/3 r³ π = 4/3 * 12 / 7 π = 16/7 π = 2.286 π cubic units

Step-by-step explanation:

The formula for normal distribution is expressed as

z = (x - u)/s

Where

u = mean

s = standard deviation

From the information given,

u = 266

s = 12

x = 242

We want to determine P(x ≥ 242). This is the probability of x greater than or equal to 242

P(x ≥ 242) = 1 - P(x </=242)

For x = 242,

z = (242 - 266)/12 = -24/12 = -2

Looking at the normal distribution table, the corresponding z score for P(x </= - 2) is 0.02275

P(x ≥ 242) = 1 - 0.02275 = 0.97725