Question

read the sentences below, filling in the blanks with items from this list. each item will be used once.
pyramid
prism
area
area
area
prism
height
cavalieris principle states that if two solids have the same
and their cross - sectional areas at all heights are equal, then their volumes are the same.
the volume of a pyramid can be calculated as one - third of the product of the base
and the height of the pyramid.
a
is a three - dimensional geometric shape that tapers smoothly from its base to a point called the apex.
the formula to calculate the volume of a pyramid is v=(1/3)×b×h, where b is the base
and h is the height of the pyramid.
to apply cavalieris principle effectively, the two compared solids must have every corresponding cross - sectional
at equal heights to be equal.
a
is a solid geometric figure whose bases or ends have the same size and shape, parallel to each other, and are joined by parallel sides.
the relationship between the volume of a pyramid and a
with the same base area and height is that the volume of the pyramid is one - third of the prisms volume.

Explanation:

1. Cavalieri's Principle requires two solids to share the same total height and matching cross-sectional areas at all heights for equal volumes.
2. The pyramid volume formula relies on the base area multiplied by height, then divided by 3.
3. A pyramid is defined as a 3D shape that narrows from a base to an apex point.
4. In the pyramid volume formula $V=\frac{1}{3}Bh$, $B$ represents the base area.
5. Cavalieri's Principle specifies that corresponding cross-sectional areas at equal heights must be equal for the solids.
6. A prism is a 3D figure with two identical, parallel bases connected by parallel sides.
7. A pyramid with the same base area and height as a prism has a volume equal to one-third of the prism's volume.

Answer:

1. height
2. area
3. pyramid
4. area
5. area
6. prism
7. prism