What is the approximate total surface area of the solid?
Consider the following data: A solid consisting of a right circular cone of radius x and height 2x standing on a hemisphere of radius x (take \pi=\frac{22}{7})
- A. 11.2x^{2}
- B. 12.5x^{2}
- C. 13.3x^{2} ✓
- D. 15.1x^{2}
Correct Answer: C. 13.3x^{2}
Explanation
TSA = CSA of cone + CSA of hemisphere. Slant height l = \sqrt{x^2 + (2x)^2} = x\sqrt{5}. Thus, TSA = \pi x(x\sqrt{5}) + 2\pi x^2 = \pi x^2(\sqrt{5} + 2). Using \sqrt{5} \approx 2.236, we get \frac{22}{7} x^2 (4.236) \approx 13.3x^2.
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