Lesson 115: $$ \begin{array}{l} ext { Solving word problems involving measurement of volume. } \ ext { (Competency B. 2.2) }\end{array} $$ Exercise Set A Directions: Read each given problem. Analyze and solve each problem. Write your answers in your notebook. 1. A box measure 10 cm on each side. What is the volume of the box? 2. How many cubic meters of sand can be loaded in a rectangular dump truck 2 m high, 3 m wide and 5.8 m long? 3. A swimming pool is a rectangular prism 30 m by 20 m and 5 m deep. What is the volume of the pool? 4. How many 3 cm blocks can you put inside a 6 cm by 9 cm by 27 cm wooden box? 5. The volume of a rectangular prism is $$ 240 \mathrm{~cm}^{3} $$. Its length is 4 cm and its height is 6 cm . How wide is it? 6. Which has a greater volume? A box which is $$ 12 \mathrm{~cm} x 3 \mathrm{~cm} x 8 \mathrm{~cm} $$ or a box which is 11 cm x 7 cm x 4 cm ? How much greater is it? 7. The area of the base of a pyramid is $$ 4.5 \mathrm{~m}^{2} $$ and its height is 3.5 m . What is the volume of the pyramid? 8. What is the volume of a pyramid whose base area is 254.30 em and whose height is 5 cm ? 9. A cylinder tank can hold $$ 1,416.93 \mathrm{dm}^{3} $$ of water. If it has a height of 5 dm . What is the radius of the tank?

Question

Lesson 115: $$ \begin{array}{l}	ext { Solving word problems involving measurement of volume. } \ 	ext { (Competency B. 2.2) }\end{array} $$ Exercise Set A Directions: Read each given problem. Analyze and solve each problem. Write your answers in your notebook. 1. A box measure 10 cm on each side. What is the volume of the box? 2. How many cubic meters of sand can be loaded in a rectangular dump truck 2 m high, 3 m wide and 5.8 m long? 3. A swimming pool is a rectangular prism 30 m by 20 m and 5 m deep. What is the volume of the pool? 4. How many 3 cm blocks can you put inside a 6 cm by 9 cm by 27 cm wooden box? 5. The volume of a rectangular prism is $$ 240 \mathrm{~cm}^{3} $$. Its length is 4 cm and its height is 6 cm . How wide is it? 6. Which has a greater volume? A box which is $$ 12 \mathrm{~cm} x 3 \mathrm{~cm} x 8 \mathrm{~cm} $$ or a box which is 11 cm x 7 cm x 4 cm ? How much greater is it? 7. The area of the base of a pyramid is $$ 4.5 \mathrm{~m}^{2} $$ and its height is 3.5 m . What is the volume of the pyramid? 8. What is the volume of a pyramid whose base area is 254.30 em and whose height is 5 cm ? 9. A cylinder tank can hold $$ 1,416.93 \mathrm{dm}^{3} $$ of water. If it has a height of 5 dm . What is the radius of the tank?

UpStudy AI · Accepted Answer

Sure! Let's work through each of the problems in **Exercise Set A** step-by-step.

---

### **1. A box measures 10 cm on each side. What is the volume of the box?**

**Solution:**

Since all sides of the box are equal, it's a cube.

**Volume of a cube** is calculated as:
$$
\text{Volume} = \text{side} \times \text{side} \times \text{side} = \text{side}^3
$$

Given:
$$
\text{Side length} = 10 \, \text{cm}
$$

Calculating:
$$
\text{Volume} = 10 \times 10 \times 10 = 1000 \, \text{cm}^3
$$

**Answer:** The volume of the box is **1,000 cubic centimeters**.

---

### **2. How many cubic meters of sand can be loaded in a rectangular dump truck 2 m high, 3 m wide, and 5.8 m long?**

**Solution:**

**Volume of a rectangular prism** is calculated as:
$$
\text{Volume} = \text{height} \times \text{width} \times \text{length}
$$

Given:
$$
\text{Height} = 2 \, \text{m}, \quad \text{Width} = 3 \, \text{m}, \quad \text{Length} = 5.8 \, \text{m}
$$

Calculating:
$$
\text{Volume} = 2 \times 3 \times 5.8 = 34.8 \, \text{m}^3
$$

**Answer:** The dump truck can hold **34.8 cubic meters** of sand.

---

### **3. A swimming pool is a rectangular prism 30 m by 20 m and 5 m deep. What is the volume of the pool?**

**Solution:**

**Volume of a rectangular prism**:
$$
\text{Volume} = \text{length} \times \text{width} \times \text{depth}
$$

Given:
$$
\text{Length} = 30 \, \text{m}, \quad \text{Width} = 20 \, \text{m}, \quad \text{Depth} = 5 \, \text{m}
$$

Calculating:
$$
\text{Volume} = 30 \times 20 \times 5 = 3,000 \, \text{m}^3
$$

**Answer:** The volume of the swimming pool is **3,000 cubic meters**.

---

### **4. How many 3 cm blocks can you put inside a 6 cm by 9 cm by 27 cm wooden box?**

**Solution:**

Assuming each block is a **cube** with sides of 3 cm.

First, find how many blocks fit along each dimension:
$$
\text{Along 6 cm side}: \frac{6}{3} = 2 \
\text{Along 9 cm side}: \frac{9}{3} = 3 \
\text{Along 27 cm side}: \frac{27}{3} = 9
$$

Total number of blocks:
$$
2 \times 3 \times 9 = 54
$$

**Answer:** You can fit **54 blocks** inside the wooden box.

---

### **5. The volume of a rectangular prism is $$ 240 \, \text{cm}^3 $$. Its length is 4 cm and its height is 6 cm. How wide is it?**

**Solution:**

**Volume formula**:
$$
\text{Volume} = \text{length} \times \text{width} \times \text{height}
$$

Given:
$$
\text{Volume} = 240 \, \text{cm}^3, \quad \text{Length} = 4 \, \text{cm}, \quad \text{Height} = 6 \, \text{cm}
$$

Let **width** be $$ w $$.

$$
240 = 4 \times w \times 6 \
240 = 24w \
w = \frac{240}{24} = 10 \, \text{cm}
$$

**Answer:** The width of the prism is **10 centimeters**.

---

### **6. Which has a greater volume? A box which is $$ 12 \, \text{cm} \times 3 \, \text{cm} \times 8 \, \text{cm} $$ or a box which is $$ 11 \, \text{cm} \times 7 \, \text{cm} \times 4 \, \text{cm} $$? How much greater is it?**

**Solution:**

**First Box Volume:**
$$
12 \times 3 \times 8 = 288 \, \text{cm}^3
$$

**Second Box Volume:**
$$
11 \times 7 \times 4 = 308 \, \text{cm}^3
$$

**Comparing Volumes:**
$$
308 \, \text{cm}^3 \, (\text{second box}) > 288 \, \text{cm}^3 \, (\text{first box})
$$
$$
\text{Difference} = 308 - 288 = 20 \, \text{cm}^3
$$

**Answer:** The second box ($$11 \times 7 \times 4 \, \text{cm}$$) has a greater volume by **20 cubic centimeters**.

---

### **7. The area of the base of a pyramid is $$ 4.5 \, \text{m}^2 $$ and its height is 3.5 m. What is the volume of the pyramid?**

**Solution:**

**Volume of a pyramid**:
$$
\text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height}
$$

Given:
$$
\text{Base Area} = 4.5 \, \text{m}^2, \quad \text{Height} = 3.5 \, \text{m}
$$

Calculating:
$$
\text{Volume} = \frac{1}{3} \times 4.5 \times 3.5 = \frac{1}{3} \times 15.75 = 5.25 \, \text{m}^3
$$

**Answer:** The volume of the pyramid is **5.25 cubic meters**.

---

### **8. What is the volume of a pyramid whose base area is 254.30 cm² and whose height is 5 cm?**

**Solution:**

**Volume of a pyramid**:
$$
\text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height}
$$

Given:
$$
\text{Base Area} = 254.30 \, \text{cm}^2, \quad \text{Height} = 5 \, \text{cm}
$$

Calculating:
$$
\text{Volume} = \frac{1}{3} \times 254.30 \times 5 = \frac{1}{3} \times 1271.5 = 420.5 \, \text{cm}^3
$$

**Answer:** The volume of the pyramid is **420.5 cubic centimeters**.

---

### **9. A cylinder tank can hold $$ 1,416.93 \, \text{dm}^3 $$ of water. If it has a height of 5 dm. What is the radius of the tank?**

**Solution:**

**Volume of a cylinder**:
$$
\text{Volume} = \pi r^2 h
$$

Given:
$$
\text{Volume} = 1,416.93 \, \text{dm}^3, \quad \text{Height} = 5 \, \text{dm}
$$

Solving for radius $$ r $$:
$$
1,416.93 = \pi r^2 \times 5
$$
$$
r^2 = \frac{1,416.93}{5\pi} \approx \frac{1,416.93}{15.70796} \approx 90.3
$$
$$
r = \sqrt{90.3} \approx 9.5 \, \text{dm}
$$

**Answer:** The radius of the tank is approximately **9.50 decimeters**.

---

Feel free to ask if you need further clarification on any of these problems!
**Solutions to Exercise Set A:** 1. **Volume of the box:** 1,000 cm³ 2. **Volume of sand the dump truck can hold:** 34.8 m³ 3. **Volume of the swimming pool:** 3,000 m³ 4. **Number of 3 cm blocks that can fit in the wooden box:** 54 5. **Width of the rectangular prism:** 10 cm 6. **Second box has a greater volume by 20 cm³** 7. **Volume of the pyramid:** 5.25 m³ 8. **Volume of the pyramid:** 420.5 cm³ 9. **Radius of the cylinder tank:** approximately 9.5 dm

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