# Frustum of Cone

• 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.

(Express the answer in terms of π)

• Statement of the problem

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.

• 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

Concepts to be taught

1. Lenght of frustum l=
2. CSA & TSA of frustum of cone

Gaps

1. difference between radius , height(depth) and lenght

Skills

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.

Algorthem

• Part-01
1. To calculate the Lenght of frustum

given:${\displaystyle r_{1}}$=15cm,${\displaystyle r_{2}}$=10cm, h=12cm

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

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

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

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

l=${\displaystyle {\sqrt {169}}}$

l=13cm

• Part-02
1. To calculate CSA

CSA= $\displaystyle π(r_{1}+r_{2})l$ Where l=${\displaystyle {\sqrt {h^{2}+(r_{1}-r_{2})^{2}}}}$

CSA=$\displaystyle π(15+10)13$

CSA=$\displaystyle 25 X 13 X π$

CSA=$\displaystyle 325πcm^2$

1. To calculate TSA

TSA= $\displaystyle π({(r_{1}+r_{2})l+r_{1}^2+r_{2}^2})$

TSA =$\displaystyle π({(15+ 10) 13 +15^2+10^2})$

TSA = $\displaystyle π({25X13 + 225 + 100})$

TSA = $\displaystyle ({325 + 225 + 100})π$

TSA =$\displaystyle 650πcm^2$