https://file.aiquickdraw.com/mathbot/file/1727385831105i0tdhtmt.jpg

The shape in the image is composed of a cone and a hemisphere. To find the total volume \( V \), we will calculate the volume of the cone and the hemisphere separately, and then add them together.

### 1. **Volume of the Cone:**

The formula for the volume of a cone is:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h_{\text{cone}}
\]
Where:
- \( r \) is the radius of the base of the cone.
- \( h_{\text{cone}} \) is the height of the cone.

From the image:
- Total height = \( 4.6 \, \text{cm} \)
- Height of the hemisphere = \( 3.7 \, \text{cm} \)
- So, the height of the cone is:
\[
h_{\text{cone}} = 4.6 \, \text{cm} - 3.7 \, \text{cm} = 0.9 \, \text{cm}
\]

We assume the radius of the base of the cone is equal to the radius of the hemisphere:
\[
r = 3.7 \, \text{cm}
\]

Now we can calculate the volume of the cone.

### 2. **Volume of the Hemisphere:**

The formula for the volume of a hemisphere is:
\[
V_{\text{hemisphere}} = \frac{2}{3} \pi r^3
\]
Where \( r \) is the radius of the hemisphere.

Now let me calculate both volumes and then sum them.The total volume \( V \) of the composite shape (cone + hemisphere) is approximately \( 118.99 \, \text{cm}^3 \).

Would you like further clarification or details? 

Here are some related questions to explore:

1. What would happen to the volume if the height of the cone increased?
2. How would you calculate the volume if the hemisphere's radius were halved?
3. How does the volume of a cone compare to that of a cylinder with the same radius and height?
4. What if the shape were composed of a cylinder and a hemisphere instead of a cone?
5. How does changing the base shape (cone, cylinder, etc.) affect the total volume?

**Tip**: Remember that the volume formulas for different 3D shapes often share the same base geometry terms (like \( r^2 \) for circles), so mastering these connections can simplify more complex problems.

Find the volume of a composite shape made of a cone and a hemisphere with a total height of 4.6 cm and hemisphere radius of 3.7 cm.

This problem shows how to calculate the total volume of a shape composed of a cone and a hemisphere with a total height of 4.6 cm and a hemisphere radius of 3.7 cm. Learn the step-by-step process using the volume formulas for cones and hemispheres.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation