Answer:
Cylinder: V ≈ [tex]50.27 cm^3[/tex]
Step-by-step explanation:
We need to find the volume of the three solids.
CONE
The volume of a cone is given as:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
where r = radius
h = height
The radius of the cone is 5 cm (since its diameter is 10 cm) and its height is 12 cm.
Therefore, its volume is:
[tex]V = \frac{1}{3} \pi * 5^2 * 12 \\\\V = 314.16 cm^3[/tex]
SPHERE
The volume of a sphere is given as:
[tex]V = \frac{4}{3} \pi r^3[/tex]
The radius of the sphere is 2 cm (since its diameter is 4 cm).
Therefore, the volume of the sphere is:
[tex]V = \frac{4}{3} * \pi * 2^3\\\\V = \frac{4}{3} * \pi * 8\\\\V = 33.51 cm^3[/tex]
CYLINDER
The volume of a cylinder is given as:
[tex]V = \pi r^2 h[/tex]
The radius of the cylinder is 2 cm and its height is 4 cm.
Therefore, the volume of the cylinder is:
[tex]V = \pi * 2^2 * 4\\\\V = \pi * 4 * 4\\\\V = 50.27cm^3[/tex]
The only one that gives the correct measure of the volume of the given shape is the cylinder.
