Frustum of Cone

(Express the answer in terms of π)
 * A bucket in the shape of a frustum with the top and bottom circles of rarii 15cm and 10cm. Its depth  is 12cm. Find its curved surface area and total surface area.

A bucket in the shape of a frustum with the top & bottom circles of radii 15cm and 10cm Its depth(height) is 12cm .CSA & TSA to be calculated length of frustum to be found. Concepts to be taught
 * Statement of the problem
 * Assumptions
 * 1) Student should know CSA & TSA of frustum of cone
 * 2) Student should know the value of л=22/7
 * 3) Student should know the difference between radius, height(depth),lenght
 * 4) Student should know the proper substitution simplification
 * 1) Lenght of frustum l=
 * 2) CSA & TSA of frustum of cone

Gaps
 * 1) difference between radius, height(depth) and lenght

Skills Algorthem given:$$r_{1}$$=15cm,$$r_{2}$$=10cm, h=12cm
 * 1) To imagine the frustum of a cone having unequal circles at the top & bottom.
 * 2) To imagine that the frustum a cone is having height(depth) inside & length out side.
 * Part-01
 * 1) To calculate the Lenght of frustum

Lenght of frustum l=$$\sqrt{h^2+(r_{1}-r_{2})^2}$$

l=$$\sqrt{12^2+(15-10)^2}$$

l=$$\sqrt{144+5^2}$$

l=$$\sqrt{144+25}$$

l=$$\sqrt{169}$$

l=13cm

CSA= $$ π(r_{1}+r_{2})l$$  Where  l=$$\sqrt{h^2+(r_{1}-r_{2})^2}$$
 * Part-02
 * 1) To calculate CSA

CSA=$$π(15+10)13$$

CSA=$$25 X 13 X π$$

CSA=$$325πcm^2$$ TSA= $$π({(r_{1}+r_{2})l+r_{1}^2+r_{2}^2})$$
 * 1) To calculate TSA

TSA =$$π({(15+ 10) 13 +15^2+10^2})$$

TSA = $$π({25X13 + 225 + 100})$$

TSA = $$({325 + 225 + 100})π$$

TSA =$$650πcm^2$$