Question

A cylinder and a cone have equal bases. The height of the cylinder is 2 cm and the area of its base is 64 cm². The cone is placed upon the cylinder volume of the solid figure so formed is 400 cm³. Find the total height of the figure.

Answer 1

The bases of a cone and a cylinder are equal.

∴ They have equal radii.

Let r be the radius.

Area of its base = 64 cm²

∴ πr² = 64 cm² 

And the height of cylinder h₁ = 2 cm

Volume of solid figure = 400 cm³ 

∴ The volume of the solid figure = Volume of the cylindrical Part + Volume of the conical part

∴ `pir^2h_1 + 1/3 pir^2h_2` = 400

∴ `64 xx 2 + 1/3 xx 64 xx h_2` = 400  .......[From (i)]

∴ `128 + 64/3 xx h_2` = 400

∴ `64/3 h_2` = 400 – 128

∴ `64/3 xx h_2` = 272

∴ h₂ = `(272 xx 3)/64`

h₂ = 12.75 cm

Height of figure = h₁ + h₂ = 2 + 12.75 = 14.75 cm

Hence, the height of the figure = 14.75 cm