1. Cotton candy is sold at the circus in a cylindrical bucket. The height of the bucket is 13 inches, and the radius is 5.5 inches. If the bucket does not have a lid, which of the following equations represents the surface area of the cotton candy bucket? $$ S A=\pi(5.5)^{2}+2 \pi(5.5)(13) $$ $$ S A=2 \pi(13)^{2}+2 \pi(13)(5.5) $$ $$ S A=2 \pi(5.5)^{2}+2 \pi(5.5)(13) $$ $$ S A=\pi(5.5)^{2}+\pi(5.5)(13) $$

Question

UpStudy AI · Accepted Answer

To determine the surface area of a cylindrical bucket without a lid, we can use the formula for the surface area of a cylinder and adjust it accordingly.

### General Formula for Surface Area of a Cylinder:
$$ S = 2\pi r^2 + 2\pi r h $$
- **$$2\pi r^2$$**: Represents the area of the top and bottom circles.
- **$$2\pi r h$$**: Represents the area of the side (the lateral surface).

### Adjusting for No Lid:
Since the bucket does not have a lid, we only have one base (bottom) instead of two. Therefore, we subtract one $$ \pi r^2 $$ from the total surface area:
$$ S = \pi r^2 + 2\pi r h $$

### Given Values:
- Height ($$ h $$) = 13 inches
- Radius ($$ r $$) = 5.5 inches

### Plugging in the Values:
$$ S = \pi (5.5)^2 + 2\pi (5.5)(13) $$

### Conclusion:
The correct equation representing the surface area of the cotton candy bucket without a lid is:
$$ S A=\pi(5.5)^{2}+2 \pi(5.5)(13) $$

**Answer:**
$$ S A=\pi(5.5)^{2}+2 \pi(5.5)(13) $$
The correct equation for the surface area of the cotton candy bucket without a lid is: $$ S A=\pi(5.5)^{2}+2 \pi(5.5)(13) $$

Cotton candy is sold at the circus in a cylindrical bucket. The height of the bucket is 13 inches, and the radius is 5.5 inches. If the bucket does not have a lid, which of the following equations represents the surface area of the cotton candy bucket?

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Solución

General Formula for Surface Area of a Cylinder:

Adjusting for No Lid:

Given Values:

Plugging in the Values:

Conclusion:

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