The diagram shows cone A which has a volume of 400 cm'
. Cone A has radius r cm and
height h cm.
Another cone, cone B, has a radius that is 150% that of cone A and a height that is 50% that of cone A. Find the capacity of cone B.

The volume \( V \) of a cone is given by the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

### Step 1: Determine the volume of Cone A
For Cone A, we know the volume is 400 cm³:

\[
V_A = 400 \, \text{cm}^3
\]

This volume is based on the radius \( r \) and height \( h \) of Cone A.

### Step 2: Express the dimensions of Cone B
- The radius of Cone B is 150% of the radius of Cone A, meaning:
  \[
  r_B = 1.5r
  \]
- The height of Cone B is 50% of the height of Cone A, meaning:
  \[
  h_B = 0.5h
  \]

### Step 3: Find the volume of Cone B
The formula for the volume of Cone B is:

\[
V_B = \frac{1}{3} \pi r_B^2 h_B
\]

Substitute \( r_B = 1.5r \) and \( h_B = 0.5h \) into the formula:

\[
V_B = \frac{1}{3} \pi (1.5r)^2 (0.5h)
\]

Simplify:

\[
V_B = \frac{1}{3} \pi (2.25r^2) (0.5h)
\]

\[
V_B = \frac{1}{3} \pi (1.125r^2 h)
\]

So the volume of Cone B is:

\[
V_B = 1.125 \times V_A
\]

### Step 4: Calculate the volume of Cone B
Since \( V_A = 400 \, \text{cm}^3 \), we can now calculate \( V_B \):

\[
V_B = 1.125 \times 400 = 450 \, \text{cm}^3
\]

### Final Answer:
The volume (capacity) of Cone B is **450 cm³**.

---

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would the volume change if the radius of Cone B were doubled instead of increased by 150%?
2. What would happen to the volume if both the radius and height of Cone B were doubled?
3. How does the volume of a cone change if only

The diagram shows cone A which has a volume of 400 cm³. Cone A has radius r cm and height h cm. Another cone, cone B, has a radius that is 150% that of cone A and a height that is 50% that of cone A. Find the capacity of cone B.

Learn how to calculate the volume of Cone B, given its radius is 150% and its height is 50% of Cone A's dimensions. This problem focuses on geometry concepts like the volume of cones and how scaling affects the capacity. Suitable for students in Grades 9-11.

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