Question

find the curved surface area of a frustum of a cone whose hight is 16cm and radii of its two ends as 8cm and 20cm respectively?

answerr plxx but right answerr..​

Answer 1

Given :-

• Height of frustum, h = 16cm

• Radius of frustum of one end, r = 8 cm

• Radius of frustum of other end, R = 20 cm

To Find :-

• Curved Surface Area of Frustum

Formula Used :-

$\red{\rm :\longmapsto\:CSA_{(frustum)} = \pi \: (R \: + \: r) \: l}$

$\blue{\rm :\longmapsto\:l \: = \: \sqrt{ {(R - r)}^{2} + {h}^{2}}}$

where,

• R = radius of upper end of frustum

• r = radius of lower end of frustum

• h = height of frustum

• l = slant height is frustum

• CSA = Curved Surface Area

Solution :-

Given that,

Height of frustum, h = 16cm

Radius of frustum of one end, r = 8 cm

Radius of frustum of other end, R = 20 cm

So,

Slant height of frustum is

$\rm :\longmapsto\:l \: = \: \sqrt{ {(R - r)}^{2} + {h}^{2} }$

$\rm :\longmapsto\:l \: = \: \sqrt{ {(20 - 8)}^{2} + {16}^{2} }$

$\rm :\longmapsto\:l \: = \: \sqrt{ {12}^{2} + {16}^{2} }$

$\rm :\longmapsto\:l \: = \: \sqrt{144+ 256}$

$\rm :\longmapsto\:l \: = \: \sqrt{400}$

$\rm :\longmapsto\:l \: = \: \sqrt{20 \times 20}$

$\bf\implies \:l = 20 \: cm$

Now,

$\rm :\longmapsto\:CSA_{(frustum)} = \pi \: (R \: + \: r) \: l$

$\rm \: \: = \: \: \pi \: (20 + 8) \times 20$

$\rm \: \: = \: \: \dfrac{22}{7} \times \: (20 + 8) \times 20$

$\rm \: \: = \: \: \dfrac{22}{7} \times \: (28) \times 20$

$\rm \: \: = \: \: 22 \times 80$

$\rm \: \: = \: \: 1760 \: {cm}^{2}$

Additional Information :-

$\rm :\longmapsto\:Volume_{(frustum)} = \dfrac{\pi \: h}{3}( {R}^{2} + {r}^{2} + Rr)$

$\rm :\longmapsto\:TSA_{(frustum)} = \pi \: \bigg((R + r)l \: + \: {R}^{2} + {r}^{2} \bigg)$