Question

Oblicz objętość graniastosłupa o wymiarach podanych na rysunku

Answer 1

In the image attached you can observe that we have three prism, we need to find their volumes. Remember, the volume of any prism is the product between its base-area and its height.

(a)

This is a trapezoidal prism, which is defined as

`V_(a)=((B+b)h_(1) )/(2) * h_(2) \\ V_(a)=((12+9)4)/(2) * 16\\ V_(a)=42 * 16 = 672 \ cm^(3)`

(b)

This is a triangular prism, which is defined as

`V_(b)=(1)/(2) b * h_(1) * h_(2)\\ V_(b)= (1)/(2) * 36 * 25 * 53\\ V_(b)=23,850 \ cm^(3)`

(c)

In this prism, 6 decimeters are equivalent to 60 centimeters. It's volume is defined as

`V=(1)/(2) * 48 * 60 * 80 = 115, 200 \ cm^(3)`