Question

pablo made an ice sculpture in the shape of this solid.
find the volume of the solid.
192 ft³

Explanation:

Step1: Split into 3 rectangular prisms

Identify the 3 separate blocks:

1. Left prism: $l=6\ \text{ft}, w=4\ \text{ft}, h=2\ \text{ft}$
2. Middle prism: $l=6\ \text{ft}, w=4\ \text{ft}, h=5-2=3\ \text{ft}$
3. Right prism: $l=6\ \text{ft}, w=4\ \text{ft}, h=8-5=3\ \text{ft}$

Step2: Calculate volume of each prism

Volume of a prism: $V = l \times w \times h$

• Left prism: $V_1 = 6 \times 4 \times 2 = 48\ \text{ft}^3$
• Middle prism: $V_2 = 6 \times 4 \times 3 = 72\ \text{ft}^3$
• Right prism: $V_3 = 6 \times 4 \times 3 = 72\ \text{ft}^3$

Step3: Sum all volumes

Add the three volumes together.
$V_{\text{total}} = V_1 + V_2 + V_3 = 48 + 72 + 72$

Answer:

$192\ \text{ft}^3$