Question

Gus is designing a cylinder to ship liquids using the constraints given.

The inside of the cylinder must hold from 475 to 480 cubic centimeters of
liquid.
The diameter must be at least 8 centimeters and at most 10 centimeters.
What are a possible radius and corresponding height, in centimeters, for the inside
of a cylinder that meets the constraints? Round the answers to the nearest tenth.
You will focus your answer on the lower constraints of 475 volume and diameter of 8
cm for our take on this problem. You will fill in the height you find rounded to the
nearest tenth with no cm. Use 3.14 for pi.

Answer 1

The possible radius and height for the inside of the cylinder that meets the constraints are r = 4 cm and h = 9.4 cm.

Explanation:

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We want to find a radius and height that will give us a volume between 475 and 480 cubic centimeters, with a diameter between 8 and 10 centimeters. First, we’ll use the lower limits of the constraints: a volume of 475 cubic centimeters and a diameter of 8 centimeters. The diameter is 8 centimeters, so the radius is 4 centimeters. We can plug in these values to the formula for volume and solve for h: 475 = 3.14 x 4^2 x h 475 = 50.24h h = 9.44 So a possible radius and height for the inside of the cylinder that meets the constraints are: r = 4 cm and h = 9.4 cm.