A basketball has a volume of 9.4 in 

3 

.  How many basketballs will fit inside of a room that is  

24 feet wide, 20 feet long, and 10 feet high?   

To determine how many basketballs will fit inside the room, we'll follow these steps:

### 1. **Calculate the volume of the room:**
   First, convert the room's dimensions from feet to inches, since the basketball's volume is given in cubic inches.

   - 1 foot = 12 inches
   - Room dimensions in inches:
     \[
     24 \text{ feet} \times 12 = 288 \text{ inches}
     \]
     \[
     20 \text{ feet} \times 12 = 240 \text{ inches}
     \]
     \[
     10 \text{ feet} \times 12 = 120 \text{ inches}
     \]

   - Volume of the room:
     \[
     288 \text{ inches} \times 240 \text{ inches} \times 120 \text{ inches} = 8,294,400 \text{ cubic inches}
     \]

### 2. **Determine how many basketballs fit inside the room:**
   Given that each basketball has a volume of 9.4 cubic inches, the number of basketballs that can fit is:
   \[
   \frac{8,294,400 \text{ cubic inches}}{9.4 \text{ cubic inches/basketball}} \approx 882,382 \text{ basketballs}
   \]

### 3. **Final Answer:**
   Approximately **882,382 basketballs** can fit inside the room, assuming perfect packing without any gaps.

Would you like more details or have any questions?

---

Here are five related questions to consider:

1. How would the number of basketballs change if the room's height was 15 feet instead of 10 feet?
2. What is the effect on the number of basketballs if their volume was 10 cubic inches instead?
3. How many basketballs would fit in a spherical room with a diameter of 24 feet?
4. How does imperfect packing (considering gaps) affect the number of basketballs that fit in the room?
5. What is the minimum room size needed to fit exactly 1,000,000 basketballs?

**Tip:** When considering packing objects in a space, account for the packing efficiency; spheres like basketballs cannot be perfectly packed into a rectangular room without leaving gaps.

Learn how to calculate how many basketballs can fit inside a room with dimensions 24 feet wide, 20 feet long, and 10 feet high using volume calculations. The solution involves converting dimensions to inches, calculating room volume, and determining the number of basketballs based on their volume. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation