f1.app.edmentum.com TAKE MY Up - Ryne... Can't Ope... (C) ClassLink... (C) CCS Class... (G) in-Googl... Unit Postt... 18 Select the correct answer from each drop-down menu. The volume of a sphere whose diameter is 18 centimeters is \( \square \) \( \pi \) cubic centimeters. If its diameter were reduced by half, its volume would be \( \square \) of its original volume. Reset Next

Let's solve the problem step by step. **1. Calculate the Volume of the Sphere with Diameter 18 cm:** The formula for the volume \( V \) of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius of the sphere. Given: - Diameter \( d = 18 \) cm - Radius \( r = \frac{d}{2} = \frac{18}{2} = 9 \) cm Plugging the values into the formula: \[ V = \frac{4}{3} \pi (9)^3 = \frac{4}{3} \pi \times 729 = 972 \pi \text{ cubic centimeters} \] **First Blank:** \( 972 \) --- **2. Calculate the New Volume When the Diameter is Reduced by Half:** If the diameter is reduced by half: - New diameter \( d' = \frac{18}{2} = 9 \) cm - New radius \( r' = \frac{9}{2} = 4.5 \) cm New volume \( V' \): \[ V' = \frac{4}{3} \pi (4.5)^3 = \frac{4}{3} \pi \times 91.125 = 121.5 \pi \text{ cubic centimeters} \] To find how \( V' \) compares to the original volume \( V \): \[ \frac{V'}{V} = \frac{121.5 \pi}{972 \pi} = \frac{121.5}{972} = \frac{1}{8} \] **Second Blank:** \( \frac{1}{8} \) --- **Final Answer:** - **First Blank:** 972 - **Second Blank:** \(\frac{1}{8}\)