Question

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 point)
• sphere = cylinder + cone
• cylinder = sphere - cone
• cone = sphere - cylinder
• cone = cylinder — sphere

Answer 1

cone = cylinder - sphere

Explanation:

the volume of a sphere is

pi×r³×4/3

the volume of a cylinder is

pi×r²×h

in our case with h = 2r

pi×r²×2r = pi×r³×2

the volume of a cone is

pi×r²×h/3

in our case with h = 2r

pi×r²×(2r)/3 = pi×r³×2/3

is

sphere = cylinder + cone ?

pi×r³×4/3 = pi×r³×2 + pi×r³×2/3

4/3 = 2 + 2/3 = 6/3 + 2/3 = 8/3 no, wrong.

is

cylinder = sphere - cone ?

pi×r³×2 = pi×r³×4/3 - pi×r³×2/3 = pi×r³×2/3 no, wrong.

is

cone = sphere - cylinder ?

pi×r³×2/3 = pi×r³×4/3 - pi×r³×2

2/3 = 4/3 - 2 = 4/3 - 6/3 = -2/3 no, wrong.

is

cone = cylinder - sphere ?

pi×r³×2/3 = pi×r³×2 - pi×r³×4/3

2/3 = 2 - 4/3 = 6/3 - 4/3 = 2/3 yes, correct.