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Question
A right angled triangle whose sides are 3 cm, 4 cm and 5 cm is revolved about the sides containing the right angle in two days. Find the difference in columes of the two cones so formed. Also, find their curved surfaces.
Solution
(i) Given that radius of cone(r1) = 4cm
Height of cone (h1) 3cm
Slant height of cone(l1) = 5cm
Volume of cone`(V_1)=1/3pir_1^2h_1`
`=1/3pi(4)^2(3)=16picm^3`
(ii) Given radius of second cone (r2) = 3cm
Height of cone(h2) = 4cm
Slant height of cone (l2) = 5cm
Volume of cone`(V_2)=1/3r_2^2h_2`
`=1/3pi(3)^2(4)=12picm^3`
Difference in volumes of two cones(V) = V1 - V2
V = 16π - 12π
V = 4πcm3
Curved surface area of first cone(S1) = πr1l1
S1 =π( 4)(5) = 20πcm2
Curved surface area of second cone(S2) = πr2l2
S2 = π(3)(5) = 15πcm2
S1 = 20πcm2 S2 = 15πcm2
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