Question

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

Explanation:

Step1: Split into 3 rectangular prisms

We divide the solid into three separate rectangular prisms, each with length 6 ft, width 4 ft, and their own heights.

Step2: Calculate height of each prism

• Prism 1 height: $2$ ft
• Prism 2 height: $5 - 2 = 3$ ft
• Prism 3 height: $8 - 5 = 3$ ft

Step3: Compute volume of each prism

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

• Prism 1: $V_1 = 6 \times 4 \times 2 = 48$ $\text{ft}^3$
• Prism 2: $V_2 = 6 \times 4 \times 3 = 72$ $\text{ft}^3$
• Prism 3: $V_3 = 6 \times 4 \times 3 = 72$ $\text{ft}^3$

Step4: Sum all prism volumes

Total volume $V = V_1 + V_2 + V_3$
$V = 48 + 72 + 72$

Answer:

$192$ $\text{ft}^3$