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.

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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