https://file.aiquickdraw.com/mathbot/file/1730500428297ko6oq7s8.jpg

You must use V= volume of cylinder + volume of hemisphere formula 

To find the volume of the figure, which combines a cylinder and a hemisphere, we need to calculate the volume of each part separately and then add them together. Here’s how we can proceed:

### Given Information:
- **Radius (r)** of the base (for both the cylinder and the hemisphere): \( r = 5 \, \text{yd} \)
- **Height (h)** of the cylinder: \( h = 8 \, \text{yd} \)
- Use \( \pi \approx 3.14 \)

### Step 1: Volume of the Cylinder
The volume \( V_{\text{cylinder}} \) of a cylinder is given by the formula:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
Substitute \( r = 5 \) and \( h = 8 \):
\[
V_{\text{cylinder}} = 3.14 \times (5)^2 \times 8
\]
\[
V_{\text{cylinder}} = 3.14 \times 25 \times 8
\]
\[
V_{\text{cylinder}} = 3.14 \times 200
\]
\[
V_{\text{cylinder}} = 628 \, \text{yd}^3
\]

### Step 2: Volume of the Hemisphere
The volume \( V_{\text{hemisphere}} \) of a hemisphere is given by:
\[
V_{\text{hemisphere}} = \frac{2}{3} \pi r^3
\]
Substitute \( r = 5 \):
\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (5)^3
\]
\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times 125
\]
\[
V_{\text{hemisphere}} = \frac{2}{3} \times 392.5
\]
\[
V_{\text{hemisphere}} \approx 261.67 \, \text{yd}^3
\]

### Step 3: Total Volume
Now, add the volumes of the cylinder and the hemisphere to find the total volume:
\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}}
\]
\[
V_{\text{total}} = 628 + 261.67
\]
\[
V_{\text{total}} \approx 889.67 \, \text{yd}^3
\]

### Answer
The total volume of the figure is approximately:
\[
\boxed{889.67 \, \text{yd}^3}
\]

Would you like further details on this solution or have any other questions?

---

Here are five related questions to expand on this concept:
1. How would the total volume change if the radius were increased to 6 yards while keeping the height the same?
2. What is the volume if only the cylinder portion was considered, excluding the hemisphere?
3. How do you calculate the surface area of this combined figure?
4. What happens to the volume if the height of the cylinder is doubled?
5. How is the formula for the volume of a hemisphere derived?

**Tip:** For composite shapes, break down the figure into simpler parts, calculate each volume individually, and then sum them up for the total volume.

Find the volume of the figure. Use 3.14 for π and round to the nearest hundredth, if necessary.

Learn how to calculate the volume of a composite figure consisting of a cylinder and a hemisphere with a detailed step-by-step solution. The radius is given as 5 yards, and the height of the cylinder is 8 yards. This problem covers key geometry concepts and volume formulas, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation