Question

Using SOLVE, determine the number of marbles that are in a large cylindrical flask as depicted in the handout from Lesson 1. Solve by hand (or electronically) and clearly outline your individual steps. (Sketch, Organized Variables, List Egns, Vary eqns, Evaluate). Embed a photo of your work below. Click the linke, for instructions to embed. Use the following variables for your evaluate step and stay in Sl units. Diameter of Marble - 13 mm Diameter of Flask - 25 cm Height of Flask (to level of marbles) - 40 cm FYI: 10 mm -1 cm

Answer 1

Given :

Diameter of the flask = 25 cm

radius, r = $\frac{25}{2}$ cm

Height of the flask, h = 40 cm

We have to find out the volume of the cylinder flask

Volume $= \pi r^2h$

           $= 3.14 \times (\frac{25}{2})^2 \times 40$

          = $19634.95 \ cm^3$

          = $19635 \ cm^3$

Now calculate the volume of the marble

Given :

Diameter = 13 mm

radius, R $=\frac{13}{2} \ mm$

Therefore, volume of the marble $=\frac{4}{3}\pi R^3$

                                                  $=\frac{4}{3}\times 3.14 \times (\frac{13}{2})^3$

                                                   $= 1150.35 \ mm^3$

                                                or  $= 115.035 \ cm^3$

Therefore, the number of the marbles $=\frac{\text{volume of flask}}{\text{volume of marble}}$

                                                          $=\frac{19635}{115.035}$

                                                        = 170.68

Therefore, the number of the marbles used is approximately 170.