If the ratio of the volumes of two right circular cylinders

[AAPL]

Veritas Prep

If the ratio of the volumes of two right circular cylinders is given by 64/9, what is the ratio of their radii? (Both cylinders have the same height)

A. 4/3
B. 8/3
C. 16/9
D. 4/1
E. 16/3

OA B

[Manasa3190]

volumes of two right circular cylinders = 64/9
ratio of their radii = ?

Volume of a right Circular cylinder = Pi*R^2*h
Given,
Both cylinders have the same height implies h1 = h2 = h
$$\frac{Pi\cdot R1^2\cdot h}{Pi\cdot R2^2\cdot h}$$ = 64/9

$$\frac{R1^2}{R2^2}$$ = 64/9
R1/R2 = 8/3

[Jay@ManhattanReview]

Veritas Prep

If the ratio of the volumes of two right circular cylinders is given by 64/9, what is the ratio of their radii? (Both cylinders have the same height)

A. 4/3
B. 8/3
C. 16/9
D. 4/1
E. 16/3

OA B

Note that the volume (V) of a right circular cylinder is given by πr^2h, where r = radius of the cylinder and h = height

So, V = πr^2h

=> Volume of proportional to the square of the radius, if height is constant

Since it is given that the two cylinders have the same heights, their volumes must be proportional to the square of the radius.

Thus, the ratio of volumes = ratio of squares of their radius

=> 64/9 = (r1/r2)^2, where r1 = radius of the bigger cylider and r2 = radius of the smaller cylider

=> r1/r2 = √(64/9) = 8/3

The correct answer: B

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

Veritas Prep

If the ratio of the volumes of two right circular cylinders is given by 64/9, what is the ratio of their radii? (Both cylinders have the same height)

A. 4/3
B. 8/3
C. 16/9
D. 4/1
E. 16/3

OA B

Let the larger radius = R and the smaller radius = r; thus, we have:

(Ï€ R^2 h)/(Ï€ r^2 h) = 64/9

R^2/r^2 = 64/9

Taking the square root of both sides, we have:

R/r = 8/3

Answer: B