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.
![### Finding the Volume of a Composite Figure
To determine the volume of the composite figure depicted, rounded to the nearest cubic foot, we need to break down the shape into simpler geometric forms, calculate the volume of each, and then sum these volumes.
The provided image shows a composite figure made up of a rectangular prism and two half-cylinders on either end. Below are the dimensions and steps to find the volume:
1. **Rectangular Prism**:
- Length: 12 feet
- Width: 4 feet
- Height: 4 feet
**Volume of the Rectangular Prism**:
\[ V_{\text{prism}} = \text{length} \times \text{width} \times \text{height} \]
\[ V_{\text{prism}} = 12 \, \text{ft} \times 4 \, \text{ft} \times 4 \, \text{ft} \]
\[ V_{\text{prism}} = 192 \, \text{cubic feet} \]
2. **Cylinders** (two halves, combined as one full cylinder):
- Radius: 2 feet (half of the width)
- Height: 4 feet (same as the width of the prism)
**Volume of One Cylinder**:
\[ V_{\text{cylinder}} = \pi \times \text{radius}^2 \times \text{height} \]
\[ V_{\text{cylinder}} = \pi \times (2 \, \text{ft})^2 \times 4 \, \text{ft} \]
\[ V_{\text{cylinder}} = \pi \times 4 \, \text{ft}^2 \times 4 \, \text{ft} \]
\[ V_{\text{cylinder}} = 16\pi \, \text{cubic feet} \]
Since the composite figure includes two halves of this cylinder:
\[ V_{\text{half-cylinders}} = 16\pi \, \text{cubic feet} \]
3. **Total Volume**:
\[ V_{\text{total}} = V_{\text{prism}} + V_{\text{half-cylinders}} \]
\[ V_{\text{total}}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e97dac8-8c85-49d8-8f7a-f33a844669bb%2Fe1300987-1036-4517-9bf1-cf9a50c13793%2Fyxrzs7c_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
