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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. - CBSE Class 10 - Mathematics

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

 NCERT Mathematics Textbook for Class 10 (with solutions)
Chapter 13: Surface Areas and Volumes
Q: 2 | Page no. 257
 R.D. Sharma 10 Mathematics (with solutions)
Chapter 16: Surface Areas and Volumes
Q: 3

Reference Material

Solution for 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. concept: Frustum of a Cone. For the course CBSE
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