Volume of Sphere
Bonus Video on Proof of Volume of Sphere
Bonus Video on Proof of Volume of Sphere
Explore!
Explore!
Use the applet to prove that the volume of a hemisphere is the same as the volume of a cylinder minus a cone.
Use the applet to prove that the volume of a hemisphere is the same as the volume of a cylinder minus a cone.
The basic idea is that the cross-sectional area of the sphere (a disc) is equal to the area of the cross-sectional area of the cylinder minus a cone (an annulus). This is shown using Pythagoras' Theorem (Click the RED Button).
The basic idea is that the cross-sectional area of the sphere (a disc) is equal to the area of the cross-sectional area of the cylinder minus a cone (an annulus). This is shown using Pythagoras' Theorem (Click the RED Button).
You can also move the RED point to change the value of the height a which is also equal to the radius of the subtracted cone.
You can also move the RED point to change the value of the height a which is also equal to the radius of the subtracted cone.
Explore!
Explore!
In this proof, we peel the sphere like an orange into pyramids of height, r. As the number of pyramids increase, the base area will tend to the surface area of the sphere.
In this proof, we peel the sphere like an orange into pyramids of height, r. As the number of pyramids increase, the base area will tend to the surface area of the sphere.
Next: Try some mensuration problems