Question
Download Solution PDFIf the radius of a sphere is thrice the radius of a hemisphere, then what will be the respective ratio of their volumes?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The radius of the hemisphere: r
Radius of the sphere: 3r
Formula:
Volume of a hemisphere = (2/3)πr3
Volume of a sphere = (4/3)π(radius)3
Calculation:
Let's calculate the respective volumes of the hemisphere and the sphere.
Volume of the hemisphere = (2/3)πr3
Volume of the sphere = (4/3)π(3r)3
Simplifying the expressions:
Volume of the hemisphere = (2/3)πr3
Volume of the sphere = (4/3)π27r3
Now, let's calculate the ratio of the volumes.
The ratio of volumes = (Volume of the sphere) / (Volume of the hemisphere)
= [(4/3)π27r3]/[(2/3)πr3]
= 54
Therefore, the respective ratio of the volumes of the sphere and the hemisphere is 54:1.
Last updated on Jul 22, 2025
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