3) A silo has a round floor with a diameter of 50 ft. It has a cylindrical body with a height of 150 ft. and the top is a hemisphere. In order to purchase enough paint to cover the floor, vertical sides and top, we must calculate the surface area of the silo. The surface area of the floor is ft?, the ft? and the surface area of the hemispherical top is surface area of the sides is ft?.
3) A silo has a round floor with a diameter of 50 ft. It has a cylindrical body with a height of 150 ft. and the top is a hemisphere. In order to purchase enough paint to cover the floor, vertical sides and top, we must calculate the surface area of the silo. The surface area of the floor is ft?, the ft? and the surface area of the hemispherical top is surface area of the sides is ft?.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:**Problem 3: Calculating the Surface Area of a Silo**
A silo has a round floor with a diameter of 50 feet. It has a cylindrical body with a height of 150 feet, and the top is a hemisphere. To purchase enough paint to cover the floor, vertical sides, and top, we must calculate the surface area of the silo.
- The surface area of the floor is ________ ft².
- The surface area of the sides is ________ ft².
- The surface area of the hemispherical top is ________ ft².
**Steps for Calculation:**
1. **Surface Area of the Floor (Circle):**
- Formula: \( A = \pi r^2 \)
- Diameter = 50 ft, thus Radius = 25 ft.
- Calculate \( A \).
2. **Surface Area of the Cylindrical Sides:**
- Formula: \( A = 2\pi rh \)
- Radius = 25 ft, Height = 150 ft.
- Calculate \( A \).
3. **Surface Area of the Hemispherical Top:**
- Formula: \( A = 2\pi r^2 \) (half of the full sphere \( 4\pi r^2 \))
- Radius = 25 ft.
- Calculate \( A \).
Sum the calculated areas to find the total surface area to be painted.
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