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प्रश्न
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
विकल्प
1 : 2
2 : 1
1 : 4
4 : 1
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उत्तर
Let the radius and height of the original cylinder be r and h respectively.
∴Volume of the original cylinder = πr2h
According to the question, radius of the new cylinder is halved keeping the height same.
⇒ Radius of the new cylinder`=r/2`
Also, height of the new cylinder = h
∴ Volume of the new cylinder `pi(r/2)^2h=(pir^2h)/4`
`\text{Volume of the new cylinder}/\text{Volume of original cylinder}=(((pir^2h)/4))/(r^2h4)=underline1=1:4`
Hence, the correct answer is C.
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Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
Maths teacher who was accompanying the students asked the following questions:
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- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
