Question

In a right circular cone, the cross-section made by a plane parallel to the base is a
(a) Circle
(b) Frustum of a cone
(c) Sphere
(d) Hemisphere

Answer 1

Hint:First we will look at the image of the cone and then we will look at what kind of shape we get if we cut the cone with a plane parallel to the base. We are going to solve this question just by cutting our cone to get a new cone.

Complete step-by-step answer:

This is the image of a right circular cone.
Let’s first look at the definition of a right circular cone to get a better understanding.
Right circular cone: A cone whose surface is generated by lines joining a fixed point to the points of a circle, the fixed point lying on a perpendicular through the centre of the circle.
Now, we will cut the cone by a plane which is parallel to the base and see what shape we get.

After cutting the cone there will be two parts one part will be a smaller coSne (upper part) and the second part will be a frustum of cone (lower part).
This is the upper part after cutting.
So, the cross-section made by a plane parallel to the base will be the same as the base of the cone.
As the base of the cone is circular, the answer will be a circle.
Hence, option (a) is correct.

Note: As it is given in the question that the plane is drawn parallel to the base of the right circular, if the plane is little tilted then it will form an ellipse, so we must be careful that this point is kept in mind.