Answer to Question #166067 in Calculus for meia

Question

1.  A hollow metal sphere has an outer diameter of 4cm and an inside diameter of 3.85 cm

a.      What is the thickness in cm?

b.     What is the outer volume cm³?

c.      What is the inner volume cm³?

d.     What is the volume of the metal sphere cm³?

Answer 1

Outer radius $R=\dfrac{\text{outer diameter}}{2}=\dfrac{4}{2}=2cm$

Inner radius $r=\dfrac{\text{Inner diameter}}{2}=\dfrac{3.85}{2}=1.925cm$

(a) Thickness=outer radius- Inner radius

$=2-1.925\\ =0.075$

(b) Outer Volume =$\dfrac{4}{3}\pi R^3$

$=\dfrac{4}{3}\times 3.14\times (2)^3$

$=\dfrac{32\times 3.14}{3}=33.51cm^3$

(C) Inner Volume =$\dfrac{4}{3}\pi r^3$

$=\dfrac{4}{3}\times 3.14\times (1.925)^3$

$=\dfrac{28.53\times 3.14}{3}=29.86cm^3$

(D) volume of Metals used= Outer Volume - Inner volume

$=33.51-29.86\\=3.645cm^3$