**Problem:**Find the surface area for the composite figure which is a cylinder with two hemispheres with a diameter of 8 inches. Leave answer in terms of π.**Dimensions:**- Diameter of hemisphere: 8 inches- Radius of hemisphere (and cylinder): 4 inches (since radius = diameter/2)- Height of the cylindrical part: 5 inches**Composite Figure Diagram:**- The composite figure includes a central cylindrical part with a height of 5 inches and two hemispheres attached to each end with a radius of 4 inches each.**Solution Approach:**1. **Surface area of the cylinder:** - Lateral surface area of a cylinder = 2πrh - Here, r = 4 inches and h = 5 inches \[ \text{Lateral surface area} = 2π(4)(5) = 40π \text{ square inches} \]2. **Surface area of the two hemispheres:** - Surface area of one hemisphere = 2πr² - Therefore, for two hemispheres: $ 2 \times 2π(4)^2 = 4π(16) = 64π \text{ square inches} $3. **Total Surface Area:** - Total Surface Area = Cylinder surface area + Surface area of two hemispheres - $ \text{Total Surface Area} = 40π + 64π = 104π \text{ square inches} $**Conclusion:**- The surface area of the composite figure is $ 104π $ square inches.For more detailed explanations or additional exercises, log in to myHRW and access the Composite Figures – Surface Area module.

Answered: Image /qna-images/answer/ffcf6a56-58ba-45a7-a931-94d1a87113d5.jpg

6. Find the surface area for the composite figure which is a cylinder with two hemispheres with diameter 8 inches. Leave answer in terms of t. Composite Figures - R Surface Area (Login to myHRW) 8 in. square inches 5 in.

6. Find the surface area for the composite figure which is a cylinder with two hemispheres with diameter 8 inches. Leave answer in terms of t. Composite Figures - R Surface Area (Login to myHRW) 8 in. square inches 5 in.

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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Concept explainers

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

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**Problem:**

Find the surface area for the composite figure which is a cylinder with two hemispheres with a diameter of 8 inches. Leave answer in terms of π.

**Dimensions:**

- Diameter of hemisphere: 8 inches
- Radius of hemisphere (and cylinder): 4 inches (since radius = diameter/2)
- Height of the cylindrical part: 5 inches

**Composite Figure Diagram:**
- The composite figure includes a central cylindrical part with a height of 5 inches and two hemispheres attached to each end with a radius of 4 inches each.

**Solution Approach:**

1. **Surface area of the cylinder:**
- Lateral surface area of a cylinder = 2πrh
- Here, r = 4 inches and h = 5 inches
\[ \text{Lateral surface area} = 2π(4)(5) = 40π \text{ square inches} \]

2. **Surface area of the two hemispheres:**
- Surface area of one hemisphere = 2πr²
- Therefore, for two hemispheres: $ 2 \times 2π(4)^2 = 4π(16) = 64π \text{ square inches} $

3. **Total Surface Area:**
- Total Surface Area = Cylinder surface area + Surface area of two hemispheres
- $ \text{Total Surface Area} = 40π + 64π = 104π \text{ square inches} $

**Conclusion:**
- The surface area of the composite figure is $ 104π $ square inches.

For more detailed explanations or additional exercises, log in to myHRW and access the Composite Figures – Surface Area module.

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