Describe how the volume

Question

formula for a cone differs
from the volume formula of
a pyramid.
choose one
Since the base of
the cone is a circle,
the volume formula
uses the area of a
circle for the base
area.
The volume of a
cone is 1/3 the
volume of a cylinder
with the same
dimensions.
The volume of a
cone is three times
the volume of a
pyramid.
The volume of a
cone is the same as
the volume of a
pyramid.

Answer 1

The correct option that describes how the volume formula for a cone differs from the volume formula of a pyramid is:

Since the base of the cone is a circle, the volume formula uses the area of a circle for the base area.

To elaborate, the volume formula for a cone is given by:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius of the circular base and \( h \) is the height of the cone.

In contrast, the volume formula for a pyramid (with a polygonal base) is:

\[ V = \frac{1}{3} \times \text{Base Area} \times h \]

In this case, the base area can be calculated differently depending on the shape of the base (e.g., triangle, square). Thus, the key difference lies in the shape of the base: the cone has a circular base, while a pyramid can have various polygonal bases.