Statements A, B, and C are true.
Step-by-step explanation:
Step 1:
A cone, a cylinder and a sphere all have radii of 3 inches. The cone and cylinder have heights of 2 inches.
The volume of the cone, [tex]V=\pi r^{2} \frac{h}{3}.[/tex] Here r = 3 inches and h = 2 inches.
So the volume of the cone [tex]=\pi r^{2} \frac{h}{3} = \pi (3^{2}) \frac{2}{3} = 18.85[/tex] cubic inches.
The volume of the cylinder, [tex]V=\pi r^{2} h.[/tex] Here r = 3 inches and h = 2 inches.
So the volume of the cylinder = [tex]=\pi r^{2} h= \pi (3^{2}) (2) = 56.55[/tex] cubic inches.
The volume of the sphere, [tex]V=\frac{4}{3} \pi r^{3}.[/tex] Here r = 3 inches.
So the volume of the sphere [tex]=\frac{4}{3} \pi (3^{3})= 113.1[/tex] cubic inches.
Step 2:
Now we check to see which statements are true.
A. About 113 cubic inches of catnip will fit inside a sphere-shaped toy so it is true.
B. About 18.8 cubic inches of catnip will fit inside a cone-shaped toy so it true.
C. The sphere-shaped toy holds the most of the three so it is true.
D. No shape holds 169.6 cubic inches, so D is false.
E. The toys shaped like a cone and a cylinder do not hold the same amount of catnip in them. So it is false.
P.S. I couldn't see the options B, D, and E completely.
