**Problem 3: Surface Area Calculation of Composite Solids**Find the surface area of the composite solids shown below. Provide your answer in square meters.**Description of the Diagram:**The given illustration displays a composite solid which is a combination of a cylinder and two cones. The dimensions are as follows:- The height of the top cone is 26 meters.- The height of the middle cylinder is 15 meters, and its radius is 12 meters.- The height of the bottom cone is 32 meters.**Explanation of the Diagram:**- The composite solid consists of a cylinder sandwiched between two cones.- The top cone has a narrow point facing upwards, measured at 26 meters in height.- The cylinder, positioned in the center, has a height of 15 meters with a radius of 12 meters.- The bottom cone points downwards and has a height of 32 meters.- The solid assumes a symmetrical shape due to the positioning of the two cones.**Calculation:**To find the surface area, add the surface area of the two cones and the curved surface area of the cylinder. Note that the top and bottom bases of the cylinder are not included in the surface area calculation since they are covered by the cones.**Surface Area Formulae Needed:**- Surface area of a cone: $ \pi r l $ where $ l $ is the slant height.- Curved surface area of a cylinder: $ 2 \pi r h $After calculating, enter the result in the box provided:\[ \boxed{\phantom{m^2}} \ \text{m}^2 \]

We have been given a figure which consists of 2 cones and a cylinder and we have to find the total…

Answered: Find the surface area of the composite…

Math

Geometry

Find the surface area of the composite solids.

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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Question

**Problem 3: Surface Area Calculation of Composite Solids**

Find the surface area of the composite solids shown below. Provide your answer in square meters.

**Description of the Diagram:**

The given illustration displays a composite solid which is a combination of a cylinder and two cones. The dimensions are as follows:

- The height of the top cone is 26 meters.
- The height of the middle cylinder is 15 meters, and its radius is 12 meters.
- The height of the bottom cone is 32 meters.

**Explanation of the Diagram:**

- The composite solid consists of a cylinder sandwiched between two cones.
- The top cone has a narrow point facing upwards, measured at 26 meters in height.
- The cylinder, positioned in the center, has a height of 15 meters with a radius of 12 meters.
- The bottom cone points downwards and has a height of 32 meters.
- The solid assumes a symmetrical shape due to the positioning of the two cones.

**Calculation:**
To find the surface area, add the surface area of the two cones and the curved surface area of the cylinder. Note that the top and bottom bases of the cylinder are not included in the surface area calculation since they are covered by the cones.

**Surface Area Formulae Needed:**
- Surface area of a cone: $ \pi r l $ where $ l $ is the slant height.
- Curved surface area of a cylinder: $ 2 \pi r h $

After calculating, enter the result in the box provided:

\[ \boxed{\phantom{m^2}} \ \text{m}^2 \]

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