If base radius of a right circular cylinder is halved , keeping the height same , find the ratio of the volume of the reduced cylinder to that of the original cylinder.
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Sólution :-
Let the radius of cylinder be r and height of cylinder be h.
Volume of cylinder is calculated by the given below formula :
Original Volume of cylinder = πr²h
As in the question it is stated that If the radius of the base of a right circular cylinder is halved keeping the height same, mathematically it can be expressed as :
New radius = ½ × r = r/2
Height = h
Hence,the reduced volume of cylinder will become as :
Reduced volume of cylinder = π × (r/2)² × h
Now, let's find the ratio of the volume of the reduced cylinder of that of the original cylinder :
⇒Required ratio = (Reduced Volume of cylinder) ÷ (Original volume of cylinder)
⇒Required ratio = (π[r/2]²h) ÷ (πr²h)
⇒Required ratio = (r/2)² ÷ r²
⇒Required ratio = (r²/4) ÷ r²
⇒Required ratio = r² ÷ (r² × 4)
⇒Required ratio = r² ÷ 4r²
⇒Required ratio = 1 ÷ 4
Hence,the required ratio of the volume of the reduced cylinder of that of the original cylinder is 1:4.
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