Question

The diameter of the base of metallic cone is 2 cm and height is 10 cm. 900 such cones are molten to form 1 right circular cylinder whose radius is 10 cm. Find total surface area of the right circular cylinder so formed. (Given $\mathrm{\pi }=3.14$)

Answer 1

Radius of the cone = $\frac{\mathrm{Diameter}}{2}=\frac{2}{2}=1\mathrm{cm}$
Height of the cone = 10 cm
Volume of the cone = $\frac{1}{3}\mathrm{\pi }{r}^{2}h$
= $\frac{1}{3}\times \mathrm{\pi }\times {\left(1\right)}^2\times 10$

Now,
Radius of the cylinder = 10 cm
Volume of the cylinder = 900 $\times$ Volume of the cone
$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^{2}h\mathit{=}900\times \frac{1}{3}\times \mathrm{\pi }\times 1^2\times 10 \\ \Rightarrow h=\frac{900\times 10}{3\times 10\times 10} \\ \Rightarrow h=30\mathrm{cm} \end{gathered}$$

Thus, we have:
Total surface area = 2$\mathrm{\pi }$r(h + r)
= 2 × 3.14 × 10 × (30 + 10)
= 2512 cm²