We appreciate your visit to The pillars in front of Mr Jefferson s home are shaped like cylinders The pillars have a height of 24 ft and a radius of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Answer:
- Option A. about 100.5ft²
Explanation:
Since the bases must not be painted, their areas are not included in the calculation.
The surface to paint, of each pillar, is equal to the lateral area of a cylinder with he dimensions given.
The formula for the laeral area of a cylinder is:
[tex]Lateral\text{ }area=2\pi \times radius \times height[/tex]
Substitute including the conversion factor to convert inches to feet:
[tex]Lateral\text{ }area=2\pi \times 8in\times 1ft/12in \times 24ft=100.5ft^2[/tex]
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The correct option is A. The surface area of a cylindrical pillar's side is calculated using the formula 2πrh. Converting the radius from inches to feet and calculating, the area is about 100.5 ft².
To calculate how many square feet of paint are needed to cover the cylindrical pillars in front of Mr. Jefferson's home, we need to find the surface area of the cylinder's side (curved surface area). The formula for the curved surface area of a cylinder is given by:
Curved Surface Area = 2πrh
Given:
- Height (h) = 24 ft
- Radius (r) = 8 inches
First, convert the radius from inches to feet:
8 inches × (1 foot / 12 inches) = 2/3 feet
Now, plug these values into the formula:
Curved Surface Area = 2 × π × (2/3) ft × 24 ft
= 2 × π × 16
= 32π
Using π ≈ 3.14, calculate the approximate value:
32 × 3.14 ≈ 100.48 ft²
So, the required square feet of paint is approximately 100.5 ft². Therefore, the answer is:
A. about 100.5 ft²
