Question

A toy is a combination of a cylinder, hemisphere and a cone, each with radius 10 cm as shown in the fig 6.48.
Height of the conical part is 10 cm and total height is 60 cm. Find the total surface area of the toy ($\mathrm{\pi }=3.14,\sqrt{2}=1.41$)

Answer 1

Given:
Radius of the cone (r) = 10 cm
Height of the conical part (h) = 10 cm
∴ Curved surface area of the cone = $\mathrm{\pi }$rl = $\mathrm{\pi }$r$\sqrt{r^2+h^2}$
= 3.14 × 10 × $\sqrt{{10}^2+{10}^2}$
= 442.74 cm²
Now,
Radius of the hemisphere = Radius of the cone = 10 cm
Thus, we have:
Curved surface area of the hemisphere = 2$\mathrm{\pi }$r²
= 2 × 3.14 × (10)²
= 628 cm²
Also,
Radius of the cone = Radius of the cylinder = 10 cm
Now,
Height of the cylindrical part = Total height – Height of the cone – Radius of the hemisphere
= 60 – 10 – 10
= 40 cm
Curved surface area of the cylinder = 2$\mathrm{\pi }$rh
= 2 × 3.14 × 10 × 40
= 2512 cm²
Thus, we have:
Total surface area of the toy = Curved surface area of the cone + Curved surface area of the hemisphere + Curved surface area of the cylinder
= (442.74 + 628 + 2512) cm²
= 3582.74 cm²