Aspherical shell has inner radius r and an outer radius r+h. let h=0.1r. find the volume of the shell in terms of r and then approximate the volume of the shell by 4πr^2h. does this seem like a reasonable approximation if h is small compared to r?

Step-by-step explanation:

The volume of the shell is the volume of the outer sphere minus the volume of the inner sphere.

V = 4/3 π (r+h)³ − 4/3 π r³

V = 4/3 π (r³ + 3r²h + 3rh² + h³) − 4/3 π r³

V = 4/3 π r³ + 4π r²h + 4π rh² + 4/3 π h³ − 4/3 π r³

V = 4π r²h + 4π rh² + 4/3 π h³

If h = 0.1 r:

V = 4π r² (0.1 r) + 4π r (0.1 r)² + 4/3 π (0.1 r)³

V = 0.4π r³ + 0.04π r³ + 0.00133π r³

V = 0.44133π r³

Using the approximation:

V = 4π r² h

V = 4π r² (0.1 r)

V = 0.4π r³

The approximation is reasonable if h is small compared to r.

n

step-by-step explanation:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500