1. The volume and area of CURVED surface of a RIGHT circular cylinder are 1540 m³ and 440m² respectively. Find the radius of the base and the height of the cylinder.Given : Volume of Cylinder → 1540 m³Curved Surface Area → 440 m²Find : Find the radius of the base and the height of the cylinder.Solution : As we know , Formulas :- From given - Now, We knowπr²h = πr × r × h PUTTING πrh as 220 From the above data : → 220r = 1540 m³r = 1540/220r = 7mSubscribe the value of " r " to find the height : πr²h = 1540→ 22/7 × (7)² × h = 1540 → 22 × 7 × h = 1540 → h = 1540 / 7 × 22→ h = 1540/154 → h = 10 m Hence, Radius of cylinder is 7 m and height of cylinder is 10 m.___________________________2. The total surface area of a right circular cylinder is 264 m² if the sum of its base and height is 10 find height.Given : Total surface area of a right circular cylinder is 264 m² The sum of its base and height is 10.Find : Find the height.Solution :As we know , Formulas :- Substituting the values in it, we get : → 2πr × 10 = 264 → 2 × 22/7 × r × 10 = 264 → r = 264 × 7/22 × 2 × 10→ r = 264 × 7/44 × 10→ r = 1848/440→ r = 4.2 m Now , For height Sum of base radius and Height → 10 m→ 4.2 + h = 10→ h = 10 - 4.2→ h = 5.8mHence , the height is 5.8 m.___________________________3. Two right circular cylinders of equal volume are such that their radii are in the ratio 4: 5 . Find the ratio of their heights.Given : Two right circular cylinders of equal volume. Radii are in the ratio 4: 5. Find : Find the ratio of their heights.Solution : As we know , Let's we consider the UNKNOWN ratio of heights be H : h Refer to the Attachment for further calculations.___________________________4. A metal cube of side 6 cm is MELTED and formed into three smaller cubes. If the sides of two smaller cubes are 3 cm , and 5 cm . find the side of third smaller cube.Given : Side of bigger cube - 6 cm Side of two smaller cube - 3 and 5 cm respectively.Find : Find the side of third smaller cube.As we know that Volume of big cube will be equal to the volume of 3 small cubes.For Volume of big cube - Now, Volume of small cubes - Cube 1 : Cube 2 :Now, Volume of 3rd smaller cube = (Volume of big cube - Volume Sum of two smaller cube)→ 216 - ( 125 + 27) → 216 - ( 152 )→ 64 cm³Now, Side = √64_________________________