Answer:
The cone has a larger volume.
Step-by-step explanation:
The volume of a cone is given by:
[tex] V_{c} = \frac{1}{3}\pi r^{2}h_{c} [/tex]
Where:
r: is the radius = 5 cm
[tex]h_{c}[/tex]: is the height of the cone = 10 cm
Then, the volume of a cone is:
[tex] V_{c} = \frac{1}{3}\pi (5 cm)^{2}*10 cm = 261.8 cm^{3} [/tex]
Now, the volume of a pyramid is:
[tex]V_{p} = \frac{1}{3}A_{b}*h_{p}[/tex]
Where:
[tex]A_{b}[/tex]: is the area of the base
[tex]h_{p}[/tex]: is the height of the pyramid = 5 cm
The area of the base can be calculated as follows:
[tex] A_{b} = l^{2} = (10 cm)^{2} = 100 cm^{2} [/tex]
Hence, the volume of the pyramid is:
[tex]V_{p} = \frac{1}{3}100 cm^{2}*5 cm = 166.7 cm^{3}[/tex]
Therefore, the cone has a larger volume.
I hope it helps you!
