Answer:
36.52 cm³
Step-by-step explanation:
You want the volume of a 7 cm long wooden toy that is a cylinder with a 2 cm high cone on one end an a hemisphere on the other end. The hemisphere and cone have the same radius as the cylinder, 1.5 cm.
Equivalent cylinder
The formula for the volume of a cylinder is ...
V = πr²h
The formula for the volume of a cone is ...
V = 1/3πr²h = πr²(h/3)
That is, a cone has the same volume as a cylinder 1/3 its height. This is 2/3h shorter than the actual height.
The formula for the volume of a hemisphere is ...
V = 2/3πr³ = πr²(2/3r)
That is, a hemisphere has the same volume as a cylinder of height equal to 2/3 the radius. This is 1/3r shorter than the actual radius.
This means we can treat the toy as a cylinder with a length that is shorter than the actual toy by (2/3·2 cm) for the cone end, and (1/3·1.5 cm) for the hemisphere end.
Volume
The volume of the toy will be ...
π(1.5 cm)²(7 cm -(2/3·2 cm) -(1/3·1.5 cm)) ≈ 36.52 cm³
The volume of the toy is about 36.52 cm³.
