Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of Tank B has a height of 8 meters and a circumference of 10 meters.
The capacity of Tank A is what percent of the capacity of Tank B?

To determine the percentage that the capacity of Tank A is relative to Tank B, we need to calculate the volumes of both tanks and then find the ratio.

### Step 1: Formula for the Volume of a Cylinder
The volume \( V \) of a right circular cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height.

### Step 2: Tank A - Volume Calculation
For Tank A, we are given:
- Height \( h_A = 10 \) meters
- Circumference of the base \( C_A = 8 \) meters

The radius \( r_A \) can be found using the formula for the circumference of a circle \( C = 2\pi r \):
\[
r_A = \frac{C_A}{2\pi} = \frac{8}{2\pi} = \frac{4}{\pi} \text{ meters}
\]

Now, we calculate the volume of Tank A:
\[
V_A = \pi r_A^2 h_A = \pi \left( \frac{4}{\pi} \right)^2 \times 10 = \pi \times \frac{16}{\pi^2} \times 10 = \frac{160}{\pi} \text{ cubic meters}
\]

### Step 3: Tank B - Volume Calculation
For Tank B, we are given:
- Height \( h_B = 8 \) meters
- Circumference of the base \( C_B = 10 \) meters

The radius \( r_B \) is:
\[
r_B = \frac{C_B}{2\pi} = \frac{10}{2\pi} = \frac{5}{\pi} \text{ meters}
\]

Now, we calculate the volume of Tank B:
\[
V_B = \pi r_B^2 h_B = \pi \left( \frac{5}{\pi} \right)^2 \times 8 = \pi \times \frac{25}{\pi^2} \times 8 = \frac{200}{\pi} \text{ cubic meters}
\]

### Step 4: Find the Percentage
The percentage that the capacity of Tank A is relative to Tank B is:
\[
\text{Percentage} = \frac{V_A}{V_B} \times 100 = \frac{\frac{160}{\pi}}{\frac{200}{\pi}} \times 100 = \frac{160}{200} \times 100 = 80\%
\]

Thus, the capacity of Tank A is **80%** of the capacity of Tank B.

---

Would you like more details on any step, or do you have any questions? Here are some related questions for practice:

1. How does changing the height of a cylinder affect its volume?
2. How does the radius of the base affect the volume of a cylinder compared to its height?
3. What would happen to the volumes if the circumferences of the tanks were doubled?
4. How can you use the volume formula to compare different geometric shapes?
5. What is the difference between lateral surface area and total surface area for a cylinder?

**Tip:** When comparing shapes, it's often helpful to reduce similar terms in the equations to make ratios clearer!

Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of Tank B has a height of 8 meters and a circumference of 10 meters. The capacity of Tank A is what percent of the capacity of Tank B?

Find out how to calculate the percentage of capacity Tank A holds relative to Tank B. This problem involves key geometric concepts, such as calculating the volume of cylinders using their height and circumference. The solution shows how to compare capacities using ratios and percentages. Suitable for students in Grades 9-12.

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