What is the CSA, TSA and volume of a frustum?

here is the answer

Let ABC be a cone. A frustum DECB is cut by a plane parallel to its base. Let r1 and r2 be the radii of the ends of the frustum of the cone and h be the height of the frustum of the cone.

In ΔABG and ΔADF, DF||BG

∴ ΔABG ∼ ΔADF

CSA of frustum DECB = CSA of cone ABC − CSA cone ADE

CSA of frustum = 

In ΔABG and ΔADF, DF||BG

∴ ΔABG ∼ ΔADF

Volume of frustum of cone = Volume of cone ABC − Volume of cone ADE

  • 57

V = frac{pi h}{3}(R_1^2+R_2^2+R_1 R_2)

begin{align}text{Lateral Surface Area}&=pi(R_1+R_2)sn&=pi(R_1+R_2)sqrt{(R_1-R_2)^2+h^2}end{align}

and

begin{align}text{Total Surface Area}&=pi((R_1+R_2)s+R_1^2+R_2^2)n&=pi((R_1+R_2)sqrt{(R_1-R_2)^2+h^2}+R_1^2+R_2^2)end{align}

  • 22
What are you looking for?