Homework Help is Here – Start Your Trial Now!
Math
Geometry
15) For a right triangular prism, suppose that the 24, and 25 ft. The altitude is 5 ft in length. a) Find the lateral area of the prism. b) Find the total area of the prism. c) Find the volume of the prism.

15) For a right triangular prism, suppose that the 24, and 25 ft. The altitude is 5 ft in length. a) Find the lateral area of the prism. b) Find the total area of the prism. c) Find the volume of the prism.

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
See similar textbooks
icon
Related questions
Question

pleaae do 15

**Educational Website Content: Mathematical Problems Related to Prisms and Cylinders** --- **Problem 15:** For a right triangular prism, suppose that the sides of the triangular base measure 7, 24, and 25 ft. The altitude is 5 ft in length. - **a) Find the lateral area of the prism.** - **b) Find the total area of the prism.** - **c) Find the volume of the prism.** **Problem 16:** For an aluminum can, the lateral surface area is \(80 \pi \, \text{in}^2\). If the length of the altitude is 6 in. greater than the length of the radius of the circular base, find the dimensions of the can. **Diagram Description:** The diagram in the image depicts a three-dimensional geometric figure. It is a right triangular prism. Below the prism, there is a graphical representation of a circular base with a vertical altitude extending through the height of the can. --- **Explanation and Calculations:** - **Right Triangular Prism Calculations:** - *Lateral Area:* This refers to the sum of the areas of the rectangular faces that are not the triangular bases. - *Total Area:* This includes the lateral area plus the area of the two triangular bases. - *Volume:* The volume is found by multiplying the area of the triangular base by the altitude of the prism. - **Aluminum Can Calculations:** - Given the lateral surface area, use the formula for the lateral surface area of a cylinder (\(2\pi rh\)), along with the relationship between the radius and the height to determine the can's dimensions. By solving these problems, students will enhance their understanding of geometric principles and their application to real-world contexts such as calculating material needs for construction or packaging.
Transcribed Image Text:**Educational Website Content: Mathematical Problems Related to Prisms and Cylinders** --- **Problem 15:** For a right triangular prism, suppose that the sides of the triangular base measure 7, 24, and 25 ft. The altitude is 5 ft in length. - **a) Find the lateral area of the prism.** - **b) Find the total area of the prism.** - **c) Find the volume of the prism.** **Problem 16:** For an aluminum can, the lateral surface area is \(80 \pi \, \text{in}^2\). If the length of the altitude is 6 in. greater than the length of the radius of the circular base, find the dimensions of the can. **Diagram Description:** The diagram in the image depicts a three-dimensional geometric figure. It is a right triangular prism. Below the prism, there is a graphical representation of a circular base with a vertical altitude extending through the height of the can. --- **Explanation and Calculations:** - **Right Triangular Prism Calculations:** - *Lateral Area:* This refers to the sum of the areas of the rectangular faces that are not the triangular bases. - *Total Area:* This includes the lateral area plus the area of the two triangular bases. - *Volume:* The volume is found by multiplying the area of the triangular base by the altitude of the prism. - **Aluminum Can Calculations:** - Given the lateral surface area, use the formula for the lateral surface area of a cylinder (\(2\pi rh\)), along with the relationship between the radius and the height to determine the can's dimensions. By solving these problems, students will enhance their understanding of geometric principles and their application to real-world contexts such as calculating material needs for construction or packaging.
Expert Solution
steps

Step by step

Solved in 5 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Anova and Design of Experiments
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS