Question

Lindor's Truffles have an outer shell diameter of 1.25 in. and a creamy milk chocolate fudge that makes up the inner circle of the ball that has a diameter of 0.5 in. How much more volume does the outer shell occupy then the inner fudge?

Answer 1

Answer:

$0.96\text{ in}^3$

Step-by-step explanation:

We have been given that Lindor's Truffles have an outer shell diameter of 1.25 in. and a creamy milk chocolate fudge that makes up the inner circle of the ball that has a diameter of 0.5 in.  

Since truffles are in shape of sphere, so we will use volume of spherical shells formula to solve our given problem.

$\text{Volume of spherical shell}=\frac{4}{3}\pi (R^3-r^3)$, where,

$R=\text{Radius of outer shell}$

$r=\text{Radius of inner shell}$

We know that radius of a circle half the diameter of circle. So we need to divide diameters of inner and outer shell by 2 to find their respective radii.

$\text{Radius of outer shell}=\frac{1.25}{2}=0.625$

$\text{Radius of inner shell}=\frac{0.5}{2}=0.25$

Upon substituting the values of radii in above formula we will get,

$\text{Volume of spherical shell}=\frac{4}{3}\pi (0.625^3-0.25^3)$

$\text{Volume of spherical shell}=\frac{4}{3}\pi (0.244140625-0.015625)$

$\text{Volume of spherical shell}=\frac{4}{3}\pi (0.228515625)$

$\text{Volume of spherical shell}=0.3046875\pi$

$\text{Volume of spherical shell}=0.95720401164\approx 0.96$

Therefore, the outer shell occupies 0.96 cubic inches of more volume than the inner fudge.

Answer 2

Answer:

0.957 in^3

Step-by-step explanation: