Question

A toy is in the form of a cone mounted on a cylinder. The diameter and height of the cylindrical part are 24cm and 35cm respectively. Base radius of cone is same as that of cylinder and total height of a toy is 40cm, then find curved surface area (C.S.A) of toy?? ​

Answer 1

Radius of a cone is $$3.5$$cm,

Height of a cone is $$15.5-3.5=12$$cm

Slant height of cone is,

$$l=\sqrt{h^2+r^2}$$

$$=\sqrt{12^2+3.5^2}$$

$$=\sqrt{144+12.25}$$

$$=\sqrt{156.25}$$

$$=12.5$$cm

Curved surface area of cone is,

$$=\pi rl$$

$$=\dfrac{22}{7}\times3.5\times12.5$$

$$=137.5cm^2$$

Curved surface area of hemispherical portion is,

$$=2\pi r^2$$

$$=2\times\dfrac{22}{7}\times3.5\times3.5$$

$$=77cm^2$$

Hence,

total surface area,

$$137.5+77=214.5cm^2$$