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A tent in the form of …

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A tent in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24m .the height of the cylindrical portion is 11m while the vertex of the cone is 16 m above the ground .find the area of canvas required for the tent.
  • 1 answers

Sia ? 6 years, 6 months ago


Diameter of cyliner = 24m
{tex}\therefore{/tex} radius of cylinder = radius of cone = 12m
Height of cylinder = 11m
Total height of tent = 16m
{tex}\therefore{/tex} Height of cone = 16-11 = 5m
Now, l2 = r2 + h2
{tex}\Rightarrow{/tex} l2 = 122 + 52
{tex}\Rightarrow{/tex} l2 = 144 + 25 = 169
{tex}\Rightarrow{/tex} l = {tex}\sqrt {169} {/tex} = 13m
{tex}\therefore{/tex} Canvas required for tent = curved surface area of cone + curved surface area of cylinder
{tex}\pi{/tex}rl + 2{tex}\pi{/tex}rh
{tex}\frac{22}{7}{/tex}{tex}\times{/tex}12{tex}\times{/tex}13+2{tex}\times{/tex}{tex}\frac{22}{7}{/tex}{tex}\times{/tex}12{tex}\times{/tex}11
{tex}\frac{22}{7}{/tex}{tex}\times{/tex}12[13+2{tex}\times{/tex}11]
=​​​​​​​ {tex}\frac{22}{7}{/tex}{tex}\times{/tex}12{tex}\times{/tex}35
= 22{tex}\times{/tex}12{tex}\times{/tex}5=1320m2

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