The solid is placed upright in a right circular cylinder full of water such that it touches the bottom. If the internal radius of cylinder is x and height is 3x, what is the approximate volume of water left in the cylinder?
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. 5.04x^{3}
- B. 5.09x^{3}
- C. 5.14x^{3}
- D. 5.24x^{3} ✓
Correct Answer: D. 5.24x^{3}
Explanation
Volume of cylinder = \pi x^2(3x) = 3\pi x^3. Volume of the solid = \frac{4}{3}\pi x^3. Water left = 3\pi x^3 - \frac{4}{3}\pi x^3 = \frac{5}{3}\pi x^3. Using \pi = \frac{22}{7}, we get \frac{5}{3} \times \frac{22}{7} x^3 = \frac{110}{21} x^3 \approx 5.24x^3.
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