Question

read the sentences below, filling in the blanks with items from this list. each item will be used once.

the principle stating that solids with equal cross - sectional areas at every height have equal volumes is called ________ principle.

the formula for the ________ of a cylinder is (v=pi r^{2}h).

the cross - sectional area of a solid is the area of a two - dimensional ________ at a given height.

the volume of a prism is found by multiplying the base area by the ________.

according to cavalieri’s principle, if two solids have the same height and their cross - sectional ________ at every level are equal, their volumes are also equal.

in the formula for the volume of a cone, the base area is multiplied by the height and then divided by ________.

the height of a cylinder is the distance between its two ________.

according to cavalieri’s principle, the volume of a slanted cylinder is the same as the volume of a ________ cylinder with the same height and radius.

the volume of a cylinder is found by multiplying the base area by the ________.

to calculate the volume of a triangular prism, you need the base area and the ________.

Explanation:

1. Identified the matching term for the geometric principle described.
2. Matched the formula to the correct 3D measurement term.
3. Defined cross-section as a 2D slice of a solid.
4. Linked prism volume calculation to the required dimension.
5. Connected Cavalieri's Principle's condition to cross-sectional measurements.
6. Recalled the cone volume formula's divisor.
7. Identified the two flat faces of a cylinder.
8. Contrasted slanted and standard cylinder types for volume equivalence.
9. Linked cylinder volume calculation to the required dimension.
10. Linked triangular prism volume calculation to the required dimension.

Answer:

1. The principle stating that solids with equal cross-sectional areas at every height have equal volumes is called Cavalieri's Principle.
2. The formula for the volume of a cylinder is $V = \pi r^2 h$.
3. The cross-sectional area of a solid is the area of a two-dimensional slice at a given height.
4. The volume of a prism is found by multiplying the base area by the height.
5. According to Cavalieri's Principle, if two solids have the same height and their cross-sectional areas at every level are equal, their volumes are also equal.
6. In the formula for the volume of a cone, the base area is multiplied by the height and then divided by three.
7. The height of a cylinder is the distance between its two bases.
8. According to Cavalieri's Principle, the volume of a slanted cylinder is the same as the volume of a straight cylinder with the same height and radius.
9. The volume of a cylinder is found by multiplying the base area by the height.
10. To calculate the volume of a triangular prism, you need the base area and the height.