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

Options

A. Circle
B. frustum of a cone
C. sphere
D. hemisphere

Explanation

To solve the question regarding the cross-section of a right circular cone made by a plane parallel to the base, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Shape**:
A right circular cone has a circular base and tapers smoothly to a point (the apex).

**Hint**: Visualize the cone and its base to understand its structure.

2. **Identify the Plane**:
The question states that a plane cuts through the cone parallel to its base. This means that the plane will not intersect the apex of the cone.

**Hint**: Imagine slicing the cone horizontally at a certain height.

3. **Analyze the Cross-Section**:
When the plane cuts through the cone parallel to the base, the shape formed at the intersection is a smaller circular section. However, the part of the cone above this section is removed, leaving a frustum shape.

**Hint**: Think about what remains of the cone after the slice is made.

4. **Define the Frustum**:
A frustum of a cone is the portion of the cone that remains after the top is cut off by a plane parallel to the base. It has two circular ends: the larger base (original base of the cone) and the smaller base (the circular cross-section made by the plane).

**Hint**: Recall the definition of a frustum and how it relates to cones.

5. **Evaluate the Options**:
- (A) Circle: Incorrect, as the cross-section is not just a circle; it is part of a frustum.
- (B) Frustum of a cone: Correct, as the cross-section forms a frustum.
- (C) Sphere: Incorrect, as the shape does not resemble a sphere.
- (D) Hemisphere: Incorrect, as the shape is not half of a sphere.

**Hint**: Compare each option with the shape you visualized.

### Conclusion:
The correct answer is (B) Frustum of a cone.