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:

$V_1=length\times width\times height$

$V_1=6\times 8\times 5$

$V_1=240$

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

The area of a triangle is:

$Area=\dfrac{1}{2}\times base\times height$

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

$B=\dfrac{1}{2}\times 8\times 4$

$B=16$

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.