Question

the slant height of a frustum of a cone is 4 cm and the perimetres of its circular ends are 18 cm and 6 cm . find the curved surface area of the frustum. answer asap

Answer 1

Slant height of frustrum = 4cm
Circumference of upper side = 18cm
2piR = 18
2×22/7×R =18
R = 18× 7/2×22
R = 63/22 cm
Circumference of lower side = 6cm
2pir = 6cm
2×22/7×r =6
r = 6×7/2×22
r = 21/2
Then, C.S.A of frustrum = pi(R+r)l
= 22/7(63/22+21/22) 4
= 22/7×84/22×4
= 12×4
= 48cm^2
Therefore,C.S.A of frustrum of cone is 48cm^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.