Question

Write down the name of the solid shape that harsha is describing. “I put two identical solid shapes together. The number of faces on the new shape is two more than the number on one of the original shapes”.

Answer 1

Hint:When we put two solid shapes together then one face of one solid shape is covered by one of the other shapes.So we need to find out the new shape combination of two identical shapes whose total face is \[2\] more than the original shape.
We will take a random variable as the number of faces of the original shape. Then applying the given condition we can get the number of faces of the original shape.

Complete step-by-step answer:
It is given that Harsha put two identical solid shapes together.
Also given that, the face of the new shape combination of two identical shapes is \[2\] more than the original shape.
We need to find out the name of the solid shape.
Let, the face of the required solid shape is \[x\].
Then by the given condition the number of faces on the new shape is \[x + 2\].
When we put two solid shapes together then one face of one solid shape is covered by one of the other shapes. So, the total face number is calculated by subtracting \[2\] faces from the solid shape faces counted twice.
Then we can say,
\[x + x - 2 = x + 2\]
\[2x - 2 = x + 2\]
\[2x - x = 2 + 2\]
\[x = 4\]
So the number of faces of the original shape is \[4\].
Therefore the solid is a tetrahedron.

Note:Objects that occupy space are called solid shapes. Their surfaces are called faces. Faces meet at edges and edges meet at vertices. Some examples of solid shapes are cone, cuboid, sphere, cylinder cube, and tetrahedron.