Question

The Skittles jar has a radius of 3.5 cm and a height of 11.5 cm. Using the two given boxes for reference what would be a good estimate for the number of jelly beans in the jar?

Answer 1

Answer:

1052

Step-by-step explanation:

The two given boxes for reference are presented below.

Since we know the dimensions of the first container, we can calculate its volume.

$V_1= 5 \text{cm} \cdot 4 \text{cm} \cdot 4 \text{cm} = 80 \text{cm}^3$

The first container held 192 skittles. Using that fact, now that we know the volume of the first box, we can calculate the volume of a single skittle.

$v = \frac{80}{192} = 0.416 \approx 0.42 \text{cm}^3$

The second container held 258 skittles.

The volume of the second box is:

$V_2 = 12 \text{cm}\cdot 3 \text{cm} \cdot 3 \text{cm} = 108 \text{cm}^3$

Using this facts, the volume of a single skittle would be

$v = \frac{108}{258} = 0.418 \approx 0.42 \text{cm}^3$

Therefore,  the volume of  single skittle is around to 0.42 cm³.

A skittle jar is a cylinder. Its volume is calculated by the formula

$V = r^2h \pi$,

where $r$ is the radius and $h$ is the height. From the given data, we have $r = 3.15 \text{cm}$ and $h = 11.5 \text{cm}$. Hence, the volume of the jar is

$V = 3.5^2 \cdot 11.5 \cdot 3.14 = 442 \text{cm}^3$

Now, we can determine the number of skittles in the jar. Let $n$ be the number of skittles in the jar. Then,

$n = \frac{\text{volume of the jar}}{\text{volume of a skittle}} = \frac{V}{v} = \frac{442}{0.42} = 1052.38 \approx 1052$