Question

The volume of a cylinder varies jointly with the square of the radius and the height. If the volume of a cylinder is 50.265 cubic inches when the radius is 2 inches and the height is 4 inches, what is the volume when the radius is 3 inches and the height is 7 inches?

Answer 1

Answer with Step-by-step explanation:

The volume of cylinder is given by

V=πr²h

Where r is the radius and h is the height

The volume of a cylinder is 50.265 cubic inches when the radius is 2 inches and the height is 4 inches.

50.265=π×2²×4

⇒ π=50.265/16

Now when r=3 inches and h=7 inches

V=π×3²×7

$V=\dfrac{50.265}{16}\times 9\times 7\\ \\V=199.336$

Hence, volume of the cylinder when the radius is 3 inches and the height is 7 inches is:

199.336 cubic inches

Answer 2

Just use the formula v = pi.(r^2).h that gives v = 9pi.7 that gives approximately 197.92 cubic inches.