Question

the slant height of a frustum of a cone is 4 cm and the perimeter of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum and the volume of frustum in terms of given measurement. Are the curved surface area and the volume of the frustum numerically equal? explain it truthfully.​

Answer 1

Step-by-step explanation:

Given:

l=4 cm

Circumference of  a circular end =18 cm

⇒2πr1=18

⇒π×r1=218=9 ...............................(1)

Circumference of other circular end  =6 cm

⇒2πr2=6

⇒πr2=26=3..........................................(2)

Adding (1) and (2)

Curved surface area 

=π(r1+r2)l

=(9+3)×4

=48 cm2

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.