Question

Derive formula for area of frustum.

Answer 1

Answer:

Step-by-step explanation:

By ratio and proportion:

L1R=LR−r

L

1

R

=

L

R

−

r

L1=RLR−r

L

1

=

R

L

R

−

r

From the figure:

L2=L1−L

L

2

=

L

1

−

L

L2=RLR−r−L

L

2

=

R

L

R

−

r

−

L

L2=RL−(R−r)LR−r

L

2

=

R

L

−

(

R

−

r

)

L

R

−

r

L2=rLR−r

L

2

=

r

L

R

−

r

The length of arc is the circumference of the base:

s1=2πR

s

1

=

2

π

R

s2=2πr

s

2

=

2

π

r

From the figure:

A=12s1L1−12s2L2

A=12(2πR)(RLR−r)−12(2πr)(rLR−r)

A=12(2πR)(RLR−r)−12(2πr) (rLR−r)

A=πR2LR−r−πr2LR−r

A=πR2LR−r−πr2LR−r

A=πR2L−πr2LR−r

A=πR2L−πr2LR−r

A=π(R2−r2)LR−r

A=π(R2−r2)LR−r

A=π(R−r)(R+r)LR−r

A=π(R−r)(RL+r)LR−r

A=π(R+r)L

A=π(R+r)L

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