Question

Among the following, which one is/are correct?
A.The slant height is the longest side of a pyramid
B.The section between the base and a plane parallel to the base of a solid is known as frustum.
C.All the surface of a cuboid are rectangular
D.For a cylinder, the top, the bottom and the walls of the cylinder determine the total surface area.

Answer 1

Hint: Here we are asked which of the given options is/are correct. Since in the question it is mentioned as is/are so there may be more than one correct option. To find out, we need to check each of the given options one by one. For the first option use the concept of cone, for the second option recall the definition of frustum, for the third option use the concept of rectangle and for the fourth option use the concept of cylinder.

Complete step-by-step answer:
To check which of the given options is/are correct. We check the options one by one.
Option (A) :- It is given that slant height is the longest side of a pyramid. Pyramid is in the shape of a cone. And the slant height of the cone is given as,
 \[l = \sqrt {{h^2} + {r^2}} \]
Therefore, we observe that slant height is greater than the height and radius of the cone. Hence, we can say slant height is the longest side of a pyramid and option (A) is correct.

Option (B) :- It is given that the section between the base and a plane parallel to the base of a solid is known as frustum. Frustum is the portion which lies between one or parallel planes in a solid. As the section lies between the base and a plane parallel to it so the section is frustum. Therefore option (B) is correct.

Option (C) :- It is given that all the surfaces of a cuboid are rectangular. In case of cuboid the length and breadth are not equal and in case of rectangular too length and breadth are not equal so, all the surfaces of a cuboid are rectangular. Therefore option (C) is correct.

Option (D) :- It is given that for a cylinder, the top, the bottom and the walls of the cylinder determine the total surface area. For the cylinder the total surface area is given as, \[S = 2\pi {r^2} + 2\pi rh\] where \[r\] is the radius and \[h\] is the height of the cylinder. The part \[2\pi {r^2}\] represents the area of top and bottom of the cylinder and the part \[2\pi rh\] represents the curved surface area of the cylinder. Therefore, we can say that for a cylinder, the top, the bottom and the walls of the cylinder determine the total surface area.
Hence, all the given options are correct.
So, the correct answer is “All the given options are correct”.

Note: For such types of questions, where more than one option may be correct we must check each of the given options separately and carefully. Here, the options were related to geometrical shapes. Always remember the concepts of basic shapes such as rectangle, square, cone, cylinder and sphere.