The ratio of the heights of a cone and a cylinder is 2 : 1 and the ratio of the radii of their bases is 3:1 respectively. Find the ratio of their volumes. :
Answers
Answered by
47
Answer:
6:1
Step-by-step explanation:
Given that the ratio of the heights of a cone and a cylinder is 2 : 1 and the ratio of the radii of their bases is 3:1 respectively. We need to find out the ratio of their volumes.
We know that volume of cone is 1/3πr²h and that of cylinder is πr²h.
Where the given value of height of cone is 2 & of cylinder is 1. While the square of radius of the cone is 9 (as r² = 3²) and of the cylinder is 1 (r² = 1²).
Now,
Volume of cone = 1/3πr²h
= 1/3 × π × (3)² × 2
= 9/3 × 2π
= 6π
Volume of cylinder = πr²h
= π × (1)² × 1
= π
Therefore,
(Volume of cone)/(Volume of cylinder) = 6π/π = 6/1
Hence, their ratios (ratio of volume of cone and that of cylinder) is 6:1.
Answered by
9
6:11 is the correct answer
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