the slant height of the frustum of a cone is 10 cm and the perimeter of its circ...

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May 2021 1 114 Report

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

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aquialaska

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 $cm^2$

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