Question

17 find the total volume of the figure below.
(figure with a rectangular prism and a pyramid on top; rectangular prism dimensions: 10 m (height), 8.8 m (width), 13.7 m (length); total height from base to pyramid apex: 25 m)

Explanation:

Step1: Calculate volume of the prism

The lower part is a rectangular prism. Volume formula: $V_{prism} = l \times w \times h$
$V_{prism} = 13.7 \times 8.8 \times 10 = 1205.6 \, \text{m}^3$

Step2: Find height of the triangular pyramid

Total height minus prism height: $25 - 10 = 15 \, \text{m}$

Step3: Calculate volume of the pyramid

Volume formula for pyramid: $V_{pyramid} = \frac{1}{3} \times l \times w \times h$
$V_{pyramid} = \frac{1}{3} \times 13.7 \times 8.8 \times 15 = 598.8 \, \text{m}^3$

Step4: Sum the two volumes

Add prism and pyramid volumes: $V_{total} = V_{prism} + V_{pyramid}$
$V_{total} = 1205.6 + 598.8 = 1804.4 \, \text{m}^3$

Answer:

$1804.4 \, \text{cubic meters}$