Question

1. what is the total volume of snow used to make the snowman if the head is 12 inches wide, the middle is 16 inches wide, and the bottom is 18 inches wide? (use 3.14 for \\(\pi\\)) 5,903.13 cubic inches 9,340.25 cubic inches 7,459.36 cubic inches 6,099.97 cubic inches

Explanation:

Step1: Recall Volume of Sphere

The snowman's parts (head, middle, bottom) are spheres. The volume of a sphere is $V = \frac{4}{3}\pi r^3$, where $r$ is the radius. Radius is half of the width (diameter).

Step2: Calculate Radius for Each Part

• Head: Width = 12 in, so $r_1=\frac{12}{2}=6$ in.
• Middle: Width = 16 in, so $r_2=\frac{16}{2}=8$ in.
• Bottom: Width = 18 in, so $r_3=\frac{18}{2}=9$ in.

Step3: Calculate Volume of Each Sphere

• Head: $V_1=\frac{4}{3}\times3.14\times6^3=\frac{4}{3}\times3.14\times216 = 904.32$ cubic inches.
• Middle: $V_2=\frac{4}{3}\times3.14\times8^3=\frac{4}{3}\times3.14\times512\approx2143.57$ cubic inches.
• Bottom: $V_3=\frac{4}{3}\times3.14\times9^3=\frac{4}{3}\times3.14\times729 = 3052.08$ cubic inches.

Step4: Total Volume

Sum the volumes: $V = V_1+V_2+V_3 = 904.32 + 2143.57+3052.08\approx6099.97$ cubic inches.

Answer:

6,099.97 cubic inches (the last option: 6,099.97 cubic inches)