SSC CGL Model Paper 18

Question : 53 of 100

Marks: +1, -0

ABC is a right angled triangle in which ∠A = 90°, AB =5 cm and AC = 12 cm. What is the approximate volume (in cm

^{3}

) of the double cone formed by rotating the triangle about its hypotenuse?

Solution:

In right angle ΔABC, by Pythagoras theorem,

(B C )^2 = (A C )^2 + (A B )^2

⇒

(B C )^2=(12)^2+(5)^2

⇒

(B C )^2 = 144 + 25 = 169

∴ BC = 13 cm
Area of

\Δ\ABC = 1/2 × AB ×AC

⇒

1/2×AO×BC=1/2×5×12

⇒

A O ×13 =60

∴

AO=60/13

Volume of double cone = Volume of first cone + volume of second cone

=1/3πr^2(CO)+1/3πr^2(OB)

=1/3πr^29CO+OB]=1/3πr^2BC

=1/3×22/7×(60/13)^2×13

= 290.10 ≈ 290 \cm^3

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