Question

a manufacturer of cat toys produces three different toys filled with catnip the toys are the shape of a cone cylinder sphere each with radius 3 inches the cone and the cylinder each have a height of 2 inches which statement about the toys are true choose all that apply help ?

Answer 1

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, $V=\pi r^{2} \frac{h}{3}.$ Here r = 3 inches and h = 2 inches.

So the volume of the cone  $=\pi r^{2} \frac{h}{3} = \pi (3^{2}) \frac{2}{3} = 18.85$ cubic inches.

The volume of the cylinder, $V=\pi r^{2} h.$ Here r = 3 inches and h = 2 inches.

So the volume of the cylinder = $=\pi r^{2} h= \pi (3^{2}) (2) = 56.55$ cubic inches.

The volume of the sphere, $V=\frac{4}{3} \pi r^{3}.$ Here r = 3 inches.

So the volume of the sphere $=\frac{4}{3} \pi (3^{3})= 113.1$ 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.