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A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 3x. Find the height of the cone in terms of y. |
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Answer» The volume of cylinder = πr²h Given that, the RADIUS of the cylinder is x and height is y. Therefore, Volume of cylinder = π(x)²y = πx²y Now, The volume of CONE = 1/3 πr²h Given that, the radius of the cone is 3X. So, the volume of cone = 1/3 π(3x)²h “A cylinder and a cone have the same volume.” According to question, ⇒ πx²y = 1/3 π(3x)²h π CANCEL out THROUGHOUT, we left with ⇒ x²y = 1/3 × 9x² × h ⇒ x²y = 3x² × h ⇒ y = (3x² × h)/x² ⇒ y = 3h ⇒ h = y/3 Therefore, the height of the cone in terms of y is y/3. |
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