(e) $$ 20 \frac{2}{3} \mathrm{~cm} imes 8 \frac{1}{3} \mathrm{~cm} imes 5 \frac{2}{3} \mathrm{~cm} $$ (g) $$ 12.5 \mathrm{~cm} imes 12.7 \mathrm{~cm} imes 2.6 \mathrm{~cm} $$

Question

(e) $$ 20 \frac{2}{3} \mathrm{~cm} 	imes 8 \frac{1}{3} \mathrm{~cm} 	imes 5 \frac{2}{3} \mathrm{~cm} $$ (g) $$ 12.5 \mathrm{~cm} 	imes 12.7 \mathrm{~cm} 	imes 2.6 \mathrm{~cm} $$

UpStudy AI · Accepted Answer

Sure, let's calculate the volumes for both parts (e) and (g) step by step.

---

### **Problem (e)**
**Dimensions:**
- Length: $$ 20 \frac{2}{3} $$ cm
- Width: $$ 8 \frac{1}{3} $$ cm
- Height: $$ 5 \frac{2}{3} $$ cm

**Step 1: Convert Mixed Numbers to Improper Fractions**

1. **Length:**
   $$
   20 \frac{2}{3} = \left(20 \times 3 + 2\right) \frac{1}{3} = \frac{62}{3} \text{ cm}
   $$
   
2. **Width:**
   $$
   8 \frac{1}{3} = \left(8 \times 3 + 1\right) \frac{1}{3} = \frac{25}{3} \text{ cm}
   $$
   
3. **Height:**
   $$
   5 \frac{2}{3} = \left(5 \times 3 + 2\right) \frac{1}{3} = \frac{17}{3} \text{ cm}
   $$

**Step 2: Calculate the Volume**

$$
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = \frac{62}{3} \times \frac{25}{3} \times \frac{17}{3}
$$

$$
\text{Volume} = \frac{62 \times 25 \times 17}{3 \times 3 \times 3} = \frac{26,350}{27} \approx 975.93 \text{ cm}^3
$$

---

### **Problem (g)**
**Dimensions:**
- Length: 12.5 cm
- Width: 12.7 cm
- Height: 2.6 cm

**Step 1: Calculate the Volume**

Since all dimensions are already in decimal form, multiply them directly:

$$
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 12.5 \times 12.7 \times 2.6
$$

**Step 2: Perform the Multiplication**

1. Multiply Length and Width:
   $$
   12.5 \times 12.7 = 158.75
   $$
   
2. Multiply the result by Height:
   $$
   158.75 \times 2.6 = 412.75 \text{ cm}^3
   $$

---

### **Final Answers**

- **Problem (e):** The volume is approximately **975.93 cm³**.
- **Problem (g):** The volume is **412.75 cm³**.
The volume for problem (e) is approximately 975.93 cm³, and for problem (g) it is 412.75 cm³.

(e)
(g)

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