Asked by stressed but well dresses

Suppose a sphere, cylinder and cone all share the same radius. The cylinder and cone also 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?

1. 3 cones + 1 cylinder
2. sphere= Cylinder + cone
3. sphere - cone= cylinder
4. 1 cylinder = 2 cones + 1 sphere
Answered by stressed but well dresses
Can you explain why this is the correct answer
Answered by stressed but well dresses
Thank you r amazing at your job
Answered by GPT 3.5
The correct option is:
4. 1 cylinder = 2 cones + 1 sphere
Answered by GPT 3.5
Certainly!

Let's compare the volume formulas for the sphere, cylinder, and cone.

The volume of a sphere with radius r is given by the formula: V_sphere = (4/3)πr^3.

The volume of a cylinder with radius r and height h is given by the formula: V_cylinder = πr^2h.

The volume of a cone with radius r and height h is given by the formula: V_cone = (1/3)πr^2h.

Given that the height of both the cylinder and cone is twice the radius, we can substitute h = 2r into the volume formulas.

Substituting h = 2r into the volume formulas for the cylinder and cone, we get:

V_cylinder = πr^2(2r) = 2πr^3,

V_cone = (1/3)πr^2(2r) = (2/3)πr^3.

Using these revised volume formulas, let's compare the volumes of 1 cylinder, 2 cones, and 1 sphere.

1 cylinder = 2πr^3,
2 cones = 2(2/3)πr^3 = (4/3)πr^3,
1 sphere = (4/3)πr^3.

We can see that the volume of 1 cylinder is equal to the sum of the volumes of 2 cones and 1 sphere. Therefore, the correct option is 4. 1 cylinder = 2 cones + 1 sphere.
Answered by GPT 3.5
You're welcome! I'm glad I could help. If you have any more questions, feel free to ask!