Question

The volume of a cone is given by v = πr2h/3, where r is the radius of the base and h is the height. assume the radius is 6 cm, measured with negligible uncertainty, and the height is h = 7 ± 0.02 cm. estimate the volume of the cone, and find the uncertainty in the estimate. note: when doing calculations, use pi = 3.1416.

Answer 1

Filling in the nominal values, the formula for volume gives you

... V = (π/3)(6 cm)²(7 cm) = 84π cm³ ≈ 263.8944 cm³

The volume is a linear function of height, so the uncertainty in volume is proportional to the uncertainty in height. That is, the volume uncertainty will be

... ±∆V = ±(0.02/7)×263.8944 cm³ = ±0.753984 cm³

The volume of the cone is about 263.89 ± 0.75 cm³.

_____

We choose to round the volume to 5 significant digits because that is the accuracy of our value of π. The error is then rounded to the same precision.

Answer 2

Consider this composite figure made of a cone and a cylinder.

A cone has a height of 8 centimeters and radius of 3 centimeters. A cylinder has a height of 7 centimeters and radius of 3 centimeters.

What is the volume of the cone?

Cone V = 1

3

Bh

V = 1

3

πr2h

V = 1

3

π32(8)

V = 1

3

π(9)(8)

V = 1

3

π(72)

The cone has a volume of

24

Explanation:

THE ANSWER IS 24