Question

The volume of a cylinder with height hh and radius rr can be found using the formula V=πr^2h. Suppose the volume of a cylinder is 1357.17 ft^3 and the height is twice the radius. What is the radius of the cylinder? Determine the radius, rounded to the nearest whole foot.

a) 7 ft
b) 10 ft
c) 15 ft
d) 20 ft

Answer 1

To find the radius, we use the formula for the volume of a cylinder and the given values. The radius of the cylinder is approximately 9.963 ft.

Step-by-step explanation:

To find the radius of the cylinder, we need to use the given volume and the relationship between the height and radius. Let's use the formula for the volume of a cylinder:

V = πr²h

Substituting the given values, we have:

1357.17 = πr²(2r)

1357.17 = 2πr³

Dividing both sides by 2π gives us:

r³ = 1357.17 / (2π)

Taking the cube root of both sides, we get:

r = (1357.17 / (2π))^(1/3)

Simplifying further, we find:

r ≈ 9.963 ft