Mathematics
Assertion (A): A sphere is inscribed in a cylinder the ratio of the volume of the cylinder to the volume of the sphere is 1 : 4.
Reason (R): Required ratio = πr2 x 2r : πr3
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
Mensuration
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Answer
Let r be the radius of the sphere.
From figure,
The radius of the cylinder is also r and the height of the cylinder is 2r.
By formula,
Volume of a cylinder (Vcylinder) = πr2h
= πr2(2r)
= 2πr3.
By formula,
Volume of a sphere (Vsphere) = πr3
Ratio of the volume of the cylinder to the volume of the sphere :
∴ A is false, but R is true.
Hence, option 2 is the correct option.
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