The volume of prism A is 72 cubic units, and the volume of prism A is twice the volume of prism B. What is the value of a? la 4. 4. 3 O A 24 о в 12 ос. 6 O D. 3
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Educational Website Content: Volume Calculation of Prisms
**Problem Description:**
The task involves calculating the missing dimension of a rectangular prism.
**Problem Statement:**
The volume of prism A is \(72\) cubic units, and the volume of prism A is twice the volume of prism B. What is the value of \(a\)?
**Answer Choices:**
- A. \(24\)
- B. \(12\)
- C. \(6\)
- D. \(3\)
**Diagram Description:**
The diagram features two rectangular prisms, labeled A and B. The dimensions of the prisms are as follows:
- **Prism A:**
- Dimensions: \(3\) (width) x \(4\) (height) x \(a\) (depth)
- **Prism B:**
- Dimensions: \(3\) (width) x \(3\) (height) x \(8a\) (depth)
**Step-by-Step Solution:**
1. **Determine the Volume of Prism B:**
Given that the volume of prism A (\(72\) cubic units) is twice the volume of prism B, we need to find the volume of prism B:
\[
\text{Volume of Prism A} = 2 \times \text{Volume of Prism B}
\]
Since the volume of Prism A is \(72\) cubic units:
\[
72 = 2 \times \text{Volume of Prism B}
\]
\[
\text{Volume of Prism B} = 36 \text{ cubic units}
\]
2. **Calculate the Missing Dimension \(a\):**
The volume of prism B can be calculated using the dimensions given:
\[
\text{Volume} = \text{width} \times \text{height} \times \text{depth}
\]
For prism B:
\[
36 = 3 \times 3 \times (8a)
\]
Simplifying this equation:
\[
36 = 9 \times (8a)
\]
\[
36 = 72a
\]
Solving for \(a\):
\[
a = \frac{36}{72}
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