Question

Answer the following questions from the given figure.

Here the solid is composed of cube, cylinder and cone.
Here,
The curved surface area of the cone is P.
The curved surface area of the cylinder is Q.
The area of the base of the cone and cylinder is R and the Total surface area of the cube is S.
Then find the total surface area of solid.
$A$. $P + Q - R + S$
$B$. $P + Q - 2R + S$
$C$. $P + Q + R + S$
$D$. $P + Q + 2R + S$

Answer 1

Hint – Here we will proceed by observing the figure carefully to find out the total surface area of solid. Then by applying the conditions given in the question we will get our answer.

Complete step by step answer:
Here, it is given that-
The curved surface area of the cone is P.
The curved surface area of the cylinder is Q.
The area of the base of cone and cylinder is R
The total surface area of the cube is S.
We have to find the total surface area of solid.
Then, the total surface area of solid is equal to –
Curved surface area of cone + Curved surface area of cylinder – Area of the cone of the cone and cylinder + Total surface area of cube.
That is, P+Q-R+S.
The upper part of the cube that is R (area of the base of the cylinder and cone) gets subtracted because it lies below the cylinder and is covered by it. So it is hidden.
Therefore, the correct option is A.
Note- Whenever we come up with this type of problem, one must know that total surface area is the surface area including the curved surface area and the base area and curved surface area is only the curved surface area excluding the base area. By using these basics, we can easily solve this question.