An amateur astronomer wishes to estimate roughly the size of the sun using his crude telescope consisting of an objective lens of focal length \(200\text{ cm}\) and an eyepiece of focal length \(10\text { cm}.\) By adjusting the distance of the eyepiece from the objective, he obtains an image of the sun on a screen \(40\text{ cm}\) behind the eyepiece.The diameter of the sun's image is measured to be \(6.0\text{ cm}.\) Now, the question is what is the estimate of the sun's size, give that the average Earth-sun distance is \(1.5 \times 10^{11}\text{ m}.\)

**Details and Assumptions**:

- Enter your answer in scientific notation. For example \(3 \times 10^8\) can be entered as \(3E+8.\)

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