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Geometry

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A spherical ball fits snugly inside a cylindrical jar, so that the ball touches the top and bottom of the jar, and the sides of the jar.  The volume of the cylinder is $144 \pi.$  What is the difference between the surface area of the sphere and the lateral surface area of the cylinder?

Mar 3, 2024

#1
+14983
+1

What is the difference between the surface area of the sphere and the lateral surface area of the cylinder?

Hello tomtom!

$$V_c =\pi r^2\cdot 2r=2\pi r^3=144\\ r=(\dfrac{72}{\pi })^{\frac{1}{3}}$$

$$LS_c=2\pi r^2+2\pi r\cdot 2r=2\pi r^2(1+2)=6\pi r^2\\ SA_s=4\pi r^2\\ LS_c-SA_s= 2\pi r^2=2\pi \cdot (\dfrac{72}{\pi })^{\frac{2}{3}} \\ \color{blue}LS_c-SA_s=50.6954$$

The surface area of the sphere and the lateral surface area of the cylinder is 50.6954.

!

Mar 3, 2024
edited by asinus  Mar 3, 2024
edited by asinus  Mar 3, 2024

#1
+14983
+1

What is the difference between the surface area of the sphere and the lateral surface area of the cylinder?

Hello tomtom!

$$V_c =\pi r^2\cdot 2r=2\pi r^3=144\\ r=(\dfrac{72}{\pi })^{\frac{1}{3}}$$

$$LS_c=2\pi r^2+2\pi r\cdot 2r=2\pi r^2(1+2)=6\pi r^2\\ SA_s=4\pi r^2\\ LS_c-SA_s= 2\pi r^2=2\pi \cdot (\dfrac{72}{\pi })^{\frac{2}{3}} \\ \color{blue}LS_c-SA_s=50.6954$$

The surface area of the sphere and the lateral surface area of the cylinder is 50.6954.

!

asinus Mar 3, 2024
edited by asinus  Mar 3, 2024
edited by asinus  Mar 3, 2024