Question

1. liana just purchased a new set of pencil crayons for an art class. each pencil crayon is cylindrical, 19.0 cm long with a diameter of 1.0 cm.

a. determine the volume of one pencil crayon in cubic centimetres. round to one decimal place.
b. the pencil crayons are sold in boxes of 12 in two rows of six. draw a diagram of the box with dimensions.
b. if each cereal box is filled to 80% capacity, what volume of cereal is in each box?

Explanation:

6. a.

Step1: Find the radius of the cylinder

The diameter $d = 1.0$ cm, so the radius $r=\frac{d}{2}=\frac{1.0}{2}=0.5$ cm.

Step2: Use the volume - formula for a cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. Given $h = 19.0$ cm and $r = 0.5$ cm, we substitute these values into the formula: $V=\pi\times(0.5)^{2}\times19.0$.

Step3: Calculate the volume

$V=\pi\times0.25\times19.0\approx3.14\times0.25\times19.0 = 14.915\approx14.9$ $cm^{3}$.

Answer:

$14.9$ $cm^{3}$

6. b.

The pencils are arranged in two rows of six.
The length of the box will be equal to the length of a pencil, $l = 19.0$ cm.
The width of the box will be the diameter of 6 pencils, $w=6\times1.0 = 6.0$ cm.
The height of the box will be the diameter of 2 pencils, $h = 2\times1.0=2.0$ cm.

To draw the diagram:

1. Draw a rectangular - box.
2. Label the length as $19.0$ cm, the width as $6.0$ cm, and the height as $2.0$ cm.

(It is not possible to actually draw the diagram in this text - based format, but the above description can be used to create the diagram.)