Suppose a sphere, cylinder, and cone all share the same radius and the cylinder and cone share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder and cone?
A. 1 cylinder = 2 cones + 1 sphere
B. sphere - cone = cylinder
C. 3 cones = 1 cylinder
D. sphere = cylinder + cone
The answer for the first question is D. Answers to Questions 2-5 that were said by Cheese Block are right.
1=cone = sphere - cylinder
2=24
3=50/3
4=36
5=24
i got answers you want
The correct answer is D. sphere = cylinder + cone.
The volume formula for a sphere is (4/3)πr^3, where r is the radius.
The volume formula for a cylinder is πr^2h, where r is the radius and h is the height.
The volume formula for a cone is (1/3)πr^2h, where r is the radius and h is the height.
Given that the cylinder and cone have the same height (which is twice the radius), we can write the volume formula for the cylinder as πr^2(2r) = 2πr^3, and the volume formula for the cone as (1/3)πr^2(2r) = (2/3)πr^3.
Adding the volume of the cylinder and the cone, we get 2πr^3 + (2/3)πr^3 = (8/3)πr^3.
Comparing this with the volume formula for the sphere (4/3)πr^3, we can see that (8/3)πr^3 = (4/3)πr^3.
Canceling out the common factor of πr^3, we are left with 8/3 = 4/3, which is not true.
Therefore, the correct relationship between the volume formulas for the sphere, cylinder, and cone is sphere = cylinder + cone.