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Find the surface area and the volume for the following regular pyramids. 10. 11. 12. slant height: 16 apothem: 4 height: 27 apothem: 9 lateral edge: 8 diagonal: 4

Find the surface area and the volume for the following regular pyramids. 10. 11. 12. slant height: 16 apothem: 4 height: 27 apothem: 9 lateral edge: 8 diagonal: 4

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Find the surface area and the volume for the following regular pyramids

### Problem: Find the Surface Area and Volume for the Following Regular Pyramids #### Pyramid 10 - **Slant Height:** 16 - **Apothem:** 4 *Diagram Explanation*: This is a regular pyramid represented with its lateral faces as triangles and a base that appears to be a polygon. The slant height (the height of each triangular face) is noted as 16 units, while the apothem (the perpendicular distance from the center of the base to a side of the base) is 4 units. #### Pyramid 11 - **Height:** 27 - **Apothem:** 9 *Diagram Explanation*: Another regular pyramid, with a central height (the perpendicular distance from the apex to the base) of 27 units and an apothem of 9 units. The base is indicated as a polygon, and the lateral faces are triangular. #### Pyramid 12 - **Lateral Edge:** 8 - **Diagonal:** 4 *Diagram Explanation*: The third regular pyramid has a given lateral edge of 8 units, which represents the slant height along the edges of the pyramid, and a diagonal length of 4 units presumably of the base. The lateral faces are triangular, and the base appears to be a polygon. ### Educational Context: This problem involves calculating the surface area and volume of regular pyramids, using provided dimensions such as slant height, height, apothem, lateral edge, and diagonal. This exercise helps students apply geometric concepts and formulas related to three-dimensional shapes. The diagrams provided give a visual representation to aid in understanding the measurements and the shape of each pyramid. --- **To Calculate Surface Area:** \[ \text{Surface Area} = \text{Base Area} + \text{Lateral Surface Area} \] For a regular pyramid: \[ \text{Lateral Surface Area} = \frac{1}{2} \times \text{Perimeter of the Base} \times \text{Slant Height} \] **To Calculate Volume:** \[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] Where the base area can be calculated based on the type of polygon forming the base. Students can engage with these formulas and solve for the given dimensions in each pyramid to find the required surface area and volume.
Transcribed Image Text:### Problem: Find the Surface Area and Volume for the Following Regular Pyramids #### Pyramid 10 - **Slant Height:** 16 - **Apothem:** 4 *Diagram Explanation*: This is a regular pyramid represented with its lateral faces as triangles and a base that appears to be a polygon. The slant height (the height of each triangular face) is noted as 16 units, while the apothem (the perpendicular distance from the center of the base to a side of the base) is 4 units. #### Pyramid 11 - **Height:** 27 - **Apothem:** 9 *Diagram Explanation*: Another regular pyramid, with a central height (the perpendicular distance from the apex to the base) of 27 units and an apothem of 9 units. The base is indicated as a polygon, and the lateral faces are triangular. #### Pyramid 12 - **Lateral Edge:** 8 - **Diagonal:** 4 *Diagram Explanation*: The third regular pyramid has a given lateral edge of 8 units, which represents the slant height along the edges of the pyramid, and a diagonal length of 4 units presumably of the base. The lateral faces are triangular, and the base appears to be a polygon. ### Educational Context: This problem involves calculating the surface area and volume of regular pyramids, using provided dimensions such as slant height, height, apothem, lateral edge, and diagonal. This exercise helps students apply geometric concepts and formulas related to three-dimensional shapes. The diagrams provided give a visual representation to aid in understanding the measurements and the shape of each pyramid. --- **To Calculate Surface Area:** \[ \text{Surface Area} = \text{Base Area} + \text{Lateral Surface Area} \] For a regular pyramid: \[ \text{Lateral Surface Area} = \frac{1}{2} \times \text{Perimeter of the Base} \times \text{Slant Height} \] **To Calculate Volume:** \[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] Where the base area can be calculated based on the type of polygon forming the base. Students can engage with these formulas and solve for the given dimensions in each pyramid to find the required surface area and volume.
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