Question

A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm² .The cone is placed up on the cylinder. Volume of the solid figure so formed is 500 cm . Find the total height of the figure

Answer 1

Given: For the cylindrical part, 

height (h) = 3 cm, 

area of the base (πr² )= 100 cm² 

Volume of the entire figure = 500 cm³ 

To find: Total height of the figure. 

A cylinder and a cone have equal bases. 

∴ they have equal radii. 

radius of cylinder = radius of cone = r Area of base = 100 cm²

∴ πr² =100 …(i) 

Let the height of the conical part be H. Volume of the entire figure = Volume of the entire + Volume of cone

∴ Height of conical part (H) =6 cm 

Total height of the figure = h + H 

= 3 + 6 = 9 cm 

∴ The total height of the figure is 9 cm.