A right triangle having sides 15 …
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Naveen Sharma 7 years, 1 month ago
Ans.
Consider the following right angled triangle ABC is rotated through its hypotenuse AC
BD {tex}\perp{/tex} AC. In this case BD is the radius of the double cone generated.
Using Pythagoras theorem for {tex}\triangle ABC{/tex}
=> AC2 = AB2 + BC
=> AC2 = 225 + 400 = 625
=> AC = 25 cm
Let AD = x cm CD = (25 – x) cm
Using Pythagoras theorem in {tex}\triangle ABD{/tex}
=> AD2 +BD2 = AB2
=> x2 + BD2= 225
=> BD2= 225 – x2 …………(1)
Using Pythagoras theorem for {tex}\triangle CBD{/tex}
=> BD2 + CD2 = BC2
=> BD2 +(25-x)2= 400
=> BD2 = 400 - (25-x)2 …………(2)
From (1) & (2)
=> 225 - x2= 400 - 625 - x2 + 50x
=> 50x = 450
=> x = 9 cm
AD = 9, CD = 16
From (1) BD = 12
Surface area of the double cone formed = L.S.A of upper cone + L.S.A of the lower cone
{tex} => \pi \times BD \times AB + \pi \times BD \times BC{/tex}
{tex} => \pi \times BD \times (AB + BC){/tex}
{tex}=> \pi \times 12(20+15){/tex}
{tex}=> \pi \times 12\times 35{/tex}
{tex}=>420 \pi {/tex}cm2
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