Question

1. communicate and justify talia claims that the surface area of the cylinder is about 2,285.92 square centimeters. explain talias error. find the correct surface area of the cylinder.

15 cm
13 cm

Explanation:

Step1: Recall cylinder surface area formula

The total surface area of a cylinder is $SA = 2\pi r^2 + 2\pi rh$, where $r$ is radius, $h$ is height.

Step2: Identify given values

$r = 13$ cm, $h = 15$ cm

Step3: Calculate area of two circular bases

$2\pi r^2 = 2\pi (13)^2 = 2\pi \times 169 = 338\pi$

Step4: Calculate lateral surface area

$2\pi rh = 2\pi \times 13 \times 15 = 390\pi$

Step5: Sum the two areas for total SA

$SA = 338\pi + 390\pi = 728\pi$

Step6: Convert to decimal approximation

$728 \times 3.1416 \approx 2287.08$

Step7: Identify Talia's error

Talia likely miscalculated the sum or used an incorrect $\pi$ approximation, or mixed up radius/height. Her value is slightly too low, suggesting a miscalculation in adding the two surface area components or a rounding error in $\pi$ (using a less precise value like 3.14 instead of 3.1416: $728\times3.14=2285.92$, which matches her answer).

Answer:

Talia's error is using a less precise approximation of $\pi$ (3.14 instead of a more accurate value like 3.1416). The correct surface area of the cylinder is approximately 2287.08 square centimeters.