Questions: Brand A Radius = 4 cm Height = 9 cm Brand B Radius = 3 cm Height = 8 cm How many more cubic centimeters does Brand A hold than Brand B ? (A) 226.08 cm^3 (B) 75.36 cm^3 (C) 25.12 cm^3 (D) 678.24 cm^3

Solution Steps

The volume \( V \) of a cone is given by the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.

For Brand A:

• Radius \( r = 4 \) cm
• Height \( h = 9 \) cm

\[ V_A = \frac{1}{3} \pi (4)^2 (9) \] \[ V_A = \frac{1}{3} \pi (16) (9) \] \[ V_A = \frac{1}{3} \pi (144) \] \[ V_A = 48 \pi \]

For Brand B:

• Radius \( r = 3 \) cm
• Height \( h = 8 \) cm

\[ V_B = \frac{1}{3} \pi (3)^2 (8) \] \[ V_B = \frac{1}{3} \pi (9) (8) \] \[ V_B = \frac{1}{3} \pi (72) \] \[ V_B = 24 \pi \]

\[ \Delta V = V_A - V_B \] \[ \Delta V = 48 \pi - 24 \pi \] \[ \Delta V = 24 \pi \]

Using \( \pi \approx 3.14 \): \[ \Delta V \approx 24 \times 3.14 \] \[ \Delta V \approx 75.36 \]

Final Answer