Math Problem Statement

Masha maakt chocoladeletters. Ze heeft 1,5 kg chocolade, dat is 1,35 liter. Hoeveel keer kan ze deze chocoladeletter maken?

Solution

To determine how many times Masha can create this chocolate letter "T," we need to calculate the volume of the "T" and then see how many times that volume fits into the total chocolate volume she has, which is 1.35 liters (or 1350 cubic centimeters, since 1 liter = 1000 cubic centimeters).

Step 1: Calculate the Volume of the Chocolate Letter "T"

The chocolate letter "T" can be divided into two rectangular prisms:

  1. The top bar.
  2. The vertical bar.

1. Volume of the Top Bar

The top bar has dimensions:

  • Width = 14 cm
  • Height = 4 cm
  • Depth = 1 cm

So, the volume of the top bar: Volumetop=14×4×1=56cm3\text{Volume}_{\text{top}} = 14 \times 4 \times 1 = 56 \, \text{cm}^3

2. Volume of the Vertical Bar

The vertical bar has dimensions:

  • Width = 4 cm
  • Height = 10 cm
  • Depth = 1 cm

So, the volume of the vertical bar: Volumevertical=4×10×1=40cm3\text{Volume}_{\text{vertical}} = 4 \times 10 \times 1 = 40 \, \text{cm}^3

Total Volume of the "T"

Total VolumeT=56+40=96cm3\text{Total Volume}_{\text{T}} = 56 + 40 = 96 \, \text{cm}^3

Step 2: Determine How Many Times This Volume Fits into 1350 cm³

Number of T’s=13509614.06\text{Number of T's} = \frac{1350}{96} \approx 14.06

Since Masha cannot make a partial chocolate letter, she can make 14 chocolate letters with 1.5 kg of chocolate.

Would you like further details or have any questions about this calculation?


Here are some follow-up questions:

  1. How would the result change if the dimensions of the chocolate letter were doubled?
  2. What if Masha had only 1 kg of chocolate instead of 1.5 kg?
  3. How would the calculation change if the chocolate density was different?
  4. Could we calculate the mass of a single chocolate letter given its volume and chocolate density?
  5. How many different ways could the "T" shape be divided to calculate the volume?

Tip: When working with volumes in cubic centimeters, remember to convert liters to cubic centimeters (1 L = 1000 cm³) to ensure consistency in measurements.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Volume calculation
Division
Geometry

Formulas

Volume of a rectangular prism = length × width × height
Total volume calculation = sum of parts
Division to determine how many times the volume fits

Theorems

-

Suitable Grade Level

Grades 7-9