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Volume of cylinderThe correct answer is: 1:2:3Explanation: We have given a hemisphere, a cylinder and a cone have equal base diameters and the same height. We have to prove that their volumes are in ration 2:3:1 Step 1 of 1:Volume of cone will be Volume of hemisphere will be Volume pf a cylinder is It is given that the hemisphere, a cylinder and a cone have equal base diameters and the same height.It means r = hSo,The ratio will be1:2:3
Solution: Given, a cone, a hemisphere and a cylinder stand on equal bases and have the same height The ratio of their volumes is 1 : 2 : 3 We have to determine if the given statement is true or false. Given, radius of cone = radius of hemisphere = radius of cylinder = r Height of cone = height of hemisphere = height of cylinder = h Volume of cone = 1/3 πr²h Volume of hemisphere = 2/3 πr³ Volume of cylinder = πr²h Ratio of volume = 1/3 πr²h : 2/3 πr³ : πr²h = 1/3 : 2/3 : 1 = 1 : 2 : 3 Therefore, the given statement is true. ✦ Try This: The circumference of the base of a cylinder is 132 cm and its height is 25 cm. The volume of the cylinder is Given, the circumference of the base of a cylinder is 132 cm Height, h = 25 cm We have to find the volume of cylinder Circumference of the base = 2πr 2πr = 132 πr = 66 r = 66/π Taking π = 22/7 r = 66 / (22/7) r = 66(7) / 22 r = 3(7) r = 21 cm Volume of cylinder = πr²h Where, r is the radius of cylinder h is the height of the cylinder So, volume = π(21)²(25) = (22/7)(441)(25) = 242550/7 = 34650 m³ Therefore, the volume of the cylinder is 34650 m³. ☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13 NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 7 Summary: The given statement “A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3” is true ☛ Related Questions: |