The area of the base of a right prism whose base is an equilateral triangle is $9\sqrt{3} {\mathrm{cm}}^2$. If the height of the prism is $12 \mathrm{cm}$, what is its lateral surface area?

Find the area of an equilateral triangle whose height is $\sqrt{48 } \mathrm{cm}$. The following steps are involved in solving the above problem. Arrange them in sequential order:

(A):$\therefore$ Area of equilateral triangle$=\frac{\sqrt{3}}{4}\times 64=16\sqrt{3}{\mathrm{cm}}^2$

(B) Let the side of the equilateral triangle be $\mathrm{a} \mathrm{cm}$.$\therefore$Height of the equilateral triangle$=\frac{\sqrt{3}a}{2}$

(C)$\therefore$ Area of an equilateral triangle whose side is $\mathrm{a} \mathrm{cm}=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times {\left(8\right)}^2\left(\because \mathrm{a}=8 \mathrm{cm}\right)$

(D) Given, $\frac{\sqrt{3}\mathrm{a}}{2}=\sqrt{48}\Rightarrow \mathrm{a}=8 \mathrm{cm}$

Find the sum of lengths of the edges  of a prism whose base is a triangle with sides $3 \mathrm{cm},4 \mathrm{cm}, 5 \mathrm{cm}$ and height is $10 \mathrm{cm}$.

The following steps are involved  in solving the above problem. Arrange them in sequential order:

(A) The sum of the lengths of the edges of a prism$=2\times \left(\mathrm{the} \mathrm{perimeter} \mathrm{of} \mathrm{base}\right)+\mathrm{number} \mathrm{of} \mathrm{sides} \mathrm{of} \mathrm{the} \mathrm{base}\times \mathrm{the} \mathrm{height} \mathrm{of} \mathrm{the} \mathrm{prism}=24+3\times 10$

(B)The perimeter of the base$=\left(3+4+5\right)\mathrm{cm}=12 \mathrm{cm}$ and the number of sides of the base is $3$.

(C)$\therefore$The sum of the lengths of the edges of a prism$=24+30=54 \mathrm{cm}$

Volume of a cone is $\mathrm{V} \mathrm{cubic} \mathrm{cm}$ and its base radius is $\mathrm{r} \mathrm{cm}$. Find its curved surface area:

The following steps are involved in solving the above problem. Arrange them in sequential order:

(A) The height of cone, $h=\frac{3V}{{\mathrm{\pi r}}^2}$

(B) Volume of a cone, $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\mathrm{V}$ and base radius$=\mathrm{r}$

(C)$\therefore$Curved surface area of the cone$=\mathrm{\pi rl}$

(D) The slant height of the cone, $\mathrm{l}=\sqrt{{\mathrm{h}}^2+{\mathrm{r}}^2}$

A conical tent is $48 \mathrm{m}$ high and the diameter of its base is $28 \mathrm{m}$. The cost of the canvas required to make the tent at the rate of $₹50$ per square metre is _____

(use $\mathrm{\pi }=\frac{22}{7}$)