Question

A toy is a combination of a cylinder, hemisphere, and a cone, each with a radius of $10$ cm as shown in the figure. The height of the conical part is $10$ cm and the total height is $60$ cm. Find the total surface area of the toy.

Answer 1

Given that the radius of a cylinder, hemisphere, and cone is $10\text{cm}$ each

The height of the conical part be $h=10\text{cm}$

The total height be $x=60\text{cm}$

Let the height of cylinder be $y=$ Total height $-$ height of the cone $-$ radius of the hemisphere

$⟹y=60-10-10=40\text{cm}$

curved surface area of cylindrical part is $2\pi ry$

$=2\pi \times 10\times 40=800\pi {\text{cm}}^2$

The surface area of hemisphere is $2\pi r^2=200\pi {\text{cm}}^2$

The surface area of cone is $\pi rl$

$=\pi \times 10\times 10\sqrt{2}=100\sqrt{2}\pi {\text{cm}}^2$ $[\because l=\sqrt{h^2+r^2}]$

$\therefore$ Total surface area will be $1000\pi +100\sqrt{2}\pi =(1000+141)\times 3.14=3582.74{\text{cm}}^2$