Math Problem Statement

Pak Hasan memiliki 30 kardus dengan ukuran 20 cm × 30 cm × 50 cm. a. Bagaimana sebaiknya Pak Hasan menyusun kardus-kardusnya agar lantai yang digunakan seminimal mungkin? b. Berapa luas lantai yang digunakan untuk menumpuk kardus-kardus tersebut? Bangun ruang gabungan terdiri dari kubus dan balok. Diketahui salah satu rusuk kubus adalah 6 cm. Sedangkan panjang, lebar, dan tinggi balok berturut-turut 5 cm, 3 cm, dan 6 cm. Tentukan volume bangun ruang gabungan tersebut!

Solution

I see the uploaded image contains some math problems. I will analyze it and provide solutions or clarifications as needed. Let me transcribe the relevant details from the image first.


Question 1:

Pak Hasan memiliki 30 kardus dengan ukuran 20 cm × 30 cm × 50 cm.
a. Bagaimana sebaiknya Pak Hasan menyusun kardus-kardusnya agar lantai yang digunakan seminimal mungkin?
b. Berapa luas lantai yang digunakan untuk menumpuk kardus-kardus tersebut?


Question 2:

Bangun ruang gabungan terdiri dari kubus dan balok.
Diketahui salah satu rusuk kubus adalah 6 cm.
Sedangkan panjang, lebar, dan tinggi balok berturut-turut 5 cm, 3 cm, dan 6 cm. Tentukan volume bangun ruang gabungan tersebut!

Jawaban (already partially given):

  1. Vbalok=P×L×T=5cm×3cm×6cm=90cm3V_{\text{balok}} = P \times L \times T = 5 \, \text{cm} \times 3 \, \text{cm} \times 6 \, \text{cm} = 90 \, \text{cm}^3
  2. Vkubus=S×S×S=6cm×6cm×6cm=216cm3V_{\text{kubus}} = S \times S \times S = 6 \, \text{cm} \times 6 \, \text{cm} \times 6 \, \text{cm} = 216 \, \text{cm}^3

Combined Volume:
Vtotal=Vbalok+Vkubus=90cm3+216cm3=306cm3V_{\text{total}} = V_{\text{balok}} + V_{\text{kubus}} = 90 \, \text{cm}^3 + 216 \, \text{cm}^3 = 306 \, \text{cm}^3.


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5 Related Questions:

  1. How can Pak Hasan minimize the height of the stack instead of the floor area?
  2. How do you calculate the surface area of the combined solid in Question 2?
  3. If Pak Hasan added more boxes, how would the floor area change?
  4. What happens to the total volume if the cube’s edge length increases by 50%?
  5. Can you find the total surface area of the combined shape (cube + block)?

Tip: For combined solids, always analyze shared boundaries if surface area calculations are needed!

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Math Problem Analysis

Mathematical Concepts

Volume of 3D Shapes
Optimization of Area
Combination of Solids

Formulas

Volume of a cuboid: V = P × L × T
Volume of a cube: V = S × S × S
Area of a rectangle: A = P × L

Theorems

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Suitable Grade Level

Grades 6-8