Question

the slant height of the frustum of a cone is 10 cm and the perimeter of its circular ends are 48 and 34 cm find the curved surface area of the frustum​

Answer 1

Answer:

Surface are of Frustum = 410 $cm^2$

Step-by-step explanation:

Given: Slant height of Frustum = 10 cm

          Perimeter of frustums circular ends = 48 cm and 34 cm

To find: Curved Surface area of frustum

Let $r_1$ be the radius of smaller circle and $r_2$ be the radius of Bigger Circle.

Perimeter of Smaller Circle = 34 cm

                                  $2\pi r_1$ = 34

                                  $\frac{22}{7}\times r_1$ = $\frac{34}{2}$

                                  $r_1$ = $17\times\frac{7}{22}$

                                  $r_1$ = $\times\frac{119}{22}\:cm$

Perimeter of Bigger Circle = 48 cm

                                  $2\pi r_2$ = 48

                                  $\frac{22}{7}\times r_2$ = $\frac{48}{2}$

                                  $r_2$ = $24\times\frac{7}{22}$

                                  $r_2$ = $\times\frac{168}{22}\:cm$

Curved Surface area of frustum = $\pi (r_1+r_2)l$

                                                     = $\frac{22}{7}\times(\frac{119}{22}+\frac{168}{22})\times10$

                                                     = $\frac{22}{7}\times\frac{7}{22}\times(17+24)\times10$

                                                     = $(41)\times10$

                                                     = 410 $cm^2$

Therefore, Surface are of Frustum = 410 $cm^2$