Question

the jellybean jar has a radius of 4.8 cm and a height of 11.8 cm. what would be a reasonable lower limit for the number of jelly beans in the jar

Answer 1

Answer:

           $\large\boxed{\large\boxed{100}}$

Explanation:

This question comes with four answer choices:

• 10,000
• 100,000
• 100
• 1

You just need to find a rough estimate of the volume of the jar and the volume of one jelly bean. This is called magnitude order.

The jellybean jar is cylindrical, Thus, its volume is $\pi \times radius^2\times height$

To find the order of magnitude, you just use the numbers rounded to one signficant figure: round π to 3, the radius to 5, cm, and the height to 10:

            $Volume\approx 3cm\times (5cm)^2\times10cm=750cm^3\approx1,000cm^3$

The order of magnitude for the radius of a jellybean is 1 cm. And the order of magnitude of the volume of a sphere with a radius of 1 cm is the cube of the diameter (2cm):

             $(2cm)^3=8cm^3\approx10cm^3$

Hence, a reasonable lower limit for the number of jellybeans in the jar is:

                     $1,000cm^3/10cm^3=100$