Question

A toy is a combination of a cylinder, hemisphere and a cone, each with radius 10 cm as shown in the figure. Height of the conical part is 10 cm and total height is 60 cm. Find the total surface area of the toy.
(π=3.14, √2=1.41)

Answer 1

Radius of the conical part = Radius of the cylinderical part = Radius of hemispherical part = 10 cm
Height of conical part, h = 10 cm
Height of the cylinder, H = 60 − 10 − 10 = 40 cm
Lateral height of the cone,

\[l = \sqrt{r^2 + h^2}\]

\[ \Rightarrow l = \sqrt{{10}^2 + {10}^2} = \sqrt{100 + 100} = \sqrt{200} = 10\sqrt{2} cm\]

Total surface area of the toy = Curved surface area of the conical part + Curved surface area of the cylinderical part + Curved surface area of the hemispherical part

Curved surface area of conical part=\[\pi rl = \pi \times 10 \times 10\sqrt{2} = 100\sqrt{2}\pi {cm}^2\] 

Curved surface area of the cylinderical part = \[2\pi rh = 2\pi \times 10 \times 40 = 800\pi {cm}^2\]2πrh=2π×10×40=800π cm2">

Curved surface area of the hemispherical part =\[2\pi r^2 = 2\pi \times {10}^2 = 200\pi {cm}^2\]

∴ Total surface area of the toy
=1002π+800π+200π=1002π+1000π=100×1.41+1000×3.14=3582.74 cm2">

\[= 100\sqrt{2}\pi + 800\pi + 200\pi\]

\[ = 100\sqrt{2}\pi + 1000\pi\]

\[ = \left( 100 \times 1 . 41 + 1000 \right) \times 3 . 14\]

\[ = 3582 . 74 {cm}^2\]