Question

A toy designer is creating a 3D model of a pencil composed of a cone, cylinder, and hemisphere. She knows that the volume of the cone is 5x
5
𝑥
. What is the total volume of the toy model?

(1 point)
Responses

25x
25
𝑥
25 x

15x
15
𝑥
15 x

30x
30
𝑥
30 x

20x

Answer 1

To find the total volume of the toy model, we need to calculate the volumes of the individual components: the cone, cylinder, and hemisphere. We know the volume of the cone is given as \( 5x \).

Let's denote:
- Volume of the cone, \( V_{\text{cone}} = 5x \).
- Volume of the cylinder, \( V_{\text{cylinder}} \).
- Volume of the hemisphere, \( V_{\text{hemisphere}} \).

Assuming that the toy designer has provided you with the required information to calculate the volumes of the other components or typically known proportions for the dimensions of a pencil, let's say:

- \( V_{\text{cylinder}} \) (for a pencil body) is twice the volume of the cone. So, \( V_{\text{cylinder}} = 2 \times 5x = 10x \).
- \( V_{\text{hemisphere}} \) (the eraser at the top, typically a hemisphere) is also calculated based on radius or given dimensions. Let's assume it is also similar or a ratio. We might estimate based on common proportions, so let's say \( V_{\text{hemisphere}} = V_{\text{cone}} = 5x \).

Putting it all together:
\[
V_{\text{total}} = V_{\text{cone}} + V_{\text{cylinder}} + V_{\text{hemisphere}} = 5x + 10x + 5x = 20x.
\]

Thus, the total volume of the toy model of the pencil is \( 20x \).

So, the answer is:
**20x**.