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Solution for The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum. - CBSE Class 10 - Mathematics

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Question

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum.

Solution 1

Perimeter of upper circular end of frustum = 18 cm

r1 =18

r1 = 9/π

Perimeter of lower end of frustum = 6 cm

r2 = 6

r2 = 3/π

Slant height (l) of frustum = 4 cm

CSA of frustum = π (r1 + r2l

`=pi(9/pi+3/pi)4`

= 12x4

= 48 cm2

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

Solution 2

We have,

Perimeter of upper end, C=18cm,

Perimeter of lower end, c=6 cm and

Slant Height, l=4 cm

Let the radius of upper end be R and the radius of lower end be r.

As, C = 18 cm

⇒2πR = 18

`=> R = 18/(2pi)`

`=> R = 9/pi`cm

Similary c = 6 cm

`=> r = 6/(2pi)`

`=> r = 3/pi` cm

Curved surface area of the frustum=π(R + r)l

`=pi(9/pi + 3/pi) xx 4`

`= pi xx 12/pi xx 4`

`= 48 cm^2`

Hence, the curved surface area of the frustum is 48 cm2

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Q: 3
 NCERT Solution for Mathematics Textbook for Class 10 (2014 to Current)
Chapter 13: Surface Areas and Volumes
Ex.13.4 | Q: 2 | Page no. 257

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Solution The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum. Concept: Frustum of a Cone.
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