Question

the slant height of a frustum of a cone is 4 cm and the perimeter is of its circular ends are 18 cm and 6 cm find the radii r and R​

Answer 1

Step-by-step explanation:

Given:

l=4 cm

Circumference of a circular end =18 cm

⇒2πr

1

=18

⇒π×r

1

=

2

18

=9 ...............................(1)

Circumference of other circular end =6 cm

⇒2πr

2

=6

⇒πr

2

=

2

6

=3..........................................(2)

Adding (1) and (2)

Curved surface area

=π(r

1

+r

2

)l

=(9+3)×4

=48 cm

2

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Answer 2

Given,

Slant height of frustum of cone (l) = 4 cm

Let ratio of the top and bottom circles be r1 and r2

And given perimeters of its circular ends as 18 cm and 6 cm

⟹ 2πr1 = 18 cm; 2πr2 = 6 cm

⟹ πr1= 9 cm and πr2 = 3 cm

We know that,

Curved surface area of frustum of a cone = π(r1 + r2)l

= (πr1+πr2)l = (9 + 3) × 4

 = (12) × 4 = 48 cm2

Therefore, the curved surface area of the frustum = 48 cm2.