Question

Raddi of the top and end and base of a frustum are 28 cm and 16cm it's height is 16cm find it's slant height

Answer 1

Step-by-step explanation:

so the slant height is 20cm

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Answer 2

Solution:-

Radius of top end of a frustum R

= 28 cm

Radius of base of a frustum r =16 cm

Heights = 16 cm

Slant height of the frustum

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

$\sf \: l = \sqrt{(16) {}^{2} + ( 28 - 16) {}^{2} }$

$\sf \: l = \sqrt{256 + (12) {}^{2} }$

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

$\sf \: l = \sqrt{400}$

$\sf \: l = 20cm$

So slant height = 20cm

Important formula

i) volume of the frustum of cone

$\rm \: = \dfrac{\pi h}{3} \{R {}^{2} + {r}^{2} + Rr \}cubic \: units$

ii) Lateral surfaces area of the frustum of the cone

$\rm \: = \pi l(R + r) \: \: where \: {l}^{2} = {h}^{2} + (R - r) {}^{2} sq \: unit$

iii) Total surface area of the frustum of the cone

$\rm = \pi \{ {R}^{2} + {r}^{2} + l(R + r) \}sq \: units$