The height of one cone is 3 times the height of another cone, while its radius is half of the radius of other cone. If their total volume is 100 unit3 , then the difference in the volumes of the cones is ______ unit3.
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 14.3.
Volume of the first cone = (1/3)π(R1)2(H1)
⇒ V1 = (1/3)π((1/2) × R2)2(3 × H2)
⇒ V1 = (1/3)π(1/4)R22(3H2)
⇒ V1 = (1/4) × 3 × (1/3)πR22H2
⇒ V1 = (3/4) × V2
Total volume (V1 + V2) = 100
⇒ (3/4)V2 + V2 = 100
⇒ (7/4)V2 = 100
⇒ V2 = 100 × (4/7)
⇒ V2 = 400/7 ≈ 57.14 unit3
⇒ V1 = (3/4) × V2 = (3/4) × 400/7 ≈ 42.86 unit3
Difference V2 - V1 = 57.14 - 42.86 ≈ 14.28 unit3
∴ The difference in the volumes of the cones is approximately 14.3 unit3.