Question

Han has to build the figure below, which will serve as a counterweight, for his robotics project. Find the VOLUME of the finished object assuming it is empty inside.

Answer 1

Given:

A figure of a robotics project.

To find:

The volume of the finished object assuming it is empty inside.

Solution:

The given figure contains a triangular prism and a cuboid.

The dimensions of the cuboid are 6 cm, 8 cm and 5 cm. So, the volume of the cuboid is:

`V_1=length* width* height`

`V_1=6* 8* 5`

`V_1=240`

So, the volume of the cuboid is 240 cubic cm.

The area of a triangle is:

`Area=(1)/(2)* base* height`

So, the area of the base of the triangular prism whose base is 8 cm and height 4 cm, is:

`B=(1)/(2)* 8* 4`

`B=16`

The volume of a triangular prism is:

`V_2=Bh`

Where, B is the base area and h is the height of the prism.

The base area of the triangular prism is 16 square cm and the height is 5 cm. So, the volume of a triangular prism is:

`V_2=16(5)`

`V_2=80`

Now, the volume of the given figure is:

`V=V_1+V_2`

`V=240+80`

`V=320`

Therefore, the volume of the finished object is 320 cubic cm.