To calculate the thickness of the spherical chocolate shell, we need to find the difference in volume between the 3-cm diameter hollow shell and the 2-cm diameter solid chocolate ball.
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius.
For the 3-cm diameter hollow shell, the radius is 3/2 = 1.5 cm.
The volume of the hollow shell is V1 = (4/3)π(1.5)^3 = 14.13 cm^3.
For the 2-cm diameter solid chocolate ball, the radius is 2/2 = 1 cm.
The volume of the solid chocolate ball is V2 = (4/3)π(1)^3 = 4.19 cm^3.
The difference in volume between the hollow shell and the solid ball is V_diff = V1 - V2 = 14.13 cm^3 - 4.19 cm^3 = 9.94 cm^3.
Now, let's find the volume of the chocolate shell. Since the shell is hollow, its volume consists of the difference in volume we calculated above.
The volume of the chocolate shell is V_shell = V_diff = 9.94 cm^3.
Finally, let's calculate the thickness of the chocolate shell. The thickness can be determined by subtracting the volume of the inner cavity (which is a solid chocolate ball) from the volume of the shell and dividing by the surface area of the shell.
The surface area of a sphere is A = 4πr^2.
The surface area of the 3-cm diameter hollow shell is A1 = 4π(1.5)^2 = 28.27 cm^2.
To find the thickness, we divide the difference in volume by the surface area of the shell. The formula is:
Thickness = V_shell / A1 = 9.94 cm^3 / 28.27 cm^2 ≈ 0.351 cm.
Therefore, the spherical chocolate shells that Chock-a-Lot is selling have a thickness of approximately 0.351 cm.
In an effort to make their product seem like a better bargain, the Chock-a-Lot candy
company increased the size of their chocolate balls, from a 2-cm diameter to a 3-cm diameter,
without increasing the price. In fact, the new balls still contain the same amount of chocolate,
because they are hollow spherical shells, while the 2-cm balls are solid chocolate. How thick
are the spherical chocolate shells that Chock-a-Lot is now selling?
1 answer
1 answer