Question

The shapes of the horizontal cross sections of the cone below are all congruent

Answer 1

All Circles we get by horizontal cross section are not equal.

Explanation:

Given: A cone.

To find: Shape of Horizontal cross section of cone are all congruent or not.

Two shapes are congruent if they are equal in measure or if they overlap each other completely.

Shape of horizontal cross section of cone is CIRCLE.

Two Circles are congruent if they have same radii.

Cross section 1: Horizontal cross section of cone near the base is a large circle almost equal to radius of cone.

Cross section 2: Horizontal cross section of cone near the top is a smallest circle whose radius is almost equal to 'zero'.

Cross section 3: Horizontal Cross section of cone in middle is a circle whose radius is between top's circle and base circle.

Its clear from above that these three cross sections are not congruent as circle don't have same radii.

Therefore, All Circles we get by horizontal cross section are not equal.

Answer 2

B. False

Explanation:

We are given the statement,

'The shapes of the horizontal cross-sections of the cone are all congruent'.

Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.

Further, the radius of the circle vary depending on the position form where the cone is cut i.e.

If cut from the top, the circle is approximately equal to a point.

If cut from the middle, the radius of the circle is less than the radius of the cone.

If cut from the bottom, the radius of the circle is equal to the radius of the cone.

Now, 'two figures are congruent if they overlap each other'.

Since, the circles have different radius, they will not overlap each other.

Thus, all the cross-sections of the cone would not be congruent.

Hence, the given statement is false.