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.
![**Problem: Calculating the Width of a Cylindrical Aquarium**
A large aquarium is cylindrical and is 25 feet deep. It can hold 26,667 cubic feet (cu.ft) of water. How wide is the tank? (Round to the nearest foot.)
To solve this problem, we need to find the diameter (width) of the cylindrical aquarium.
1. **Understanding the Formula:**
The volume \( V \) of a cylinder can be calculated using the formula:
\[
V = \pi r^2 h
\]
Where:
- \( V \) is the volume of the cylinder.
- \( r \) is the radius of the cylinder’s base.
- \( h \) is the height (or depth) of the cylinder.
- \( \pi \) (pi) is a constant approximately equal to 3.14159.
2. **Given Values:**
- Volume (\( V \)) = 26,667 cubic feet
- Height (\( h \)) = 25 feet
3. **Substitute the Given Values into the Formula:**
\[
26,667 = \pi r^2 \times 25
\]
4. **Solve for \( r^2 \):**
\[
r^2 = \frac{26,667}{\pi \times 25}
\]
5. **Calculate \( r^2 \):**
\[
r^2 = \frac{26,667}{3.14159 \times 25}
\]
\[
r^2 = \frac{26,667}{78.53975} \approx 339.1
\]
6. **Solve for \( r \):**
\[
r = \sqrt{339.1} \approx 18.4
\]
7. **Calculate the Diameter (Width):**
The diameter \( d \) is twice the radius:
\[
d = 2r = 2 \times 18.4 \approx 36.8
\]
Rounded to the nearest foot, the width of the tank is approximately 37 feet.
**Answer:**
The width of the cylindrical aquarium is approximately 37 feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4895642d-adca-4243-b0c4-c741dfdd726d%2F1ce26da7-6f33-401d-8770-c2a6274aecf2%2Fzpg7ovr_processed.jpeg&w=3840&q=75)
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