Question

A few students conducted a study on how many peanuts it would take to completely fill a jar. They had the following data to help them with the study: In a container with a volume of 108 they could fit 65 peanuts. In a container with a volume of 150 they could fit 90 peanuts. The height of the jar for the peanuts is 16 cm and the radius is 3.5 cm. What number would be a good estimate for the number of peanuts in a jar this size?

Answer 1

370 peanuts

Explanation:

65/108 = 0.60185

90/150 = 0.6000

In each case, the number of peanuts is either exactly or very close to 60% of the volume.

A cylinder with radius 3.5 cm and height 16 cm has volume:

V = (pi)r^2h

V = (3.14159)(3.5 cm)^2(16 cm)

V = 615.752 cm^3

We take 60% of the volume to estimate the number of peanuts.

60% * 615.752 cm^3 = 369.451

Answer: 370 peanuts