Question

A circular cone has a base of radius 10 cm and height 25 cm. The area of the cross section of the cone by a plane parallel to its base is 154 cm square. Find the distance of the plane from the base of the cone

Answer 1

Given data:

The circular cone has a base of radius 10 cm and height 25 cm.

The area of the cross section of the cone by a plane parallel to its base is 150 cm square.

To find:

The distance of the plane from the base of the cone.

Solution:

We draw the attached figure. (Check the picture)

Let the radius of the cross section be r cm.

Then the area of the cross section is πr² cm square.

Given, πr² = 154

or, 22/7 × r² = 154

or, r² = 7/22 × 154

or, r² = 7 × 7

or, r² = 7²

or, r = 7

So, the radius of the cross section is 7 cm.

Let the distance of the plane from the base is x cm.

Then we can draw two triangles ADE and ABC, which are similar triangles.

From the property of similar triangles, we can write:

AD / AB = DE / BC

or, (25 - x) / 25 = 7 / 10

or, 10 (25 - x) = 175

or, 250 - 10x = 175

or, 10x = 75

or, x = 7.5

Answer:

Therefore the distance of the plane from the base of the cone is 7.5 cm.

Answer 2

Step-by-step explanation:

Given data:

The circular cone has a base of radius 10 cm and height 25 cm.

The area of the cross section of the cone by a plane parallel to its base is 150 cm square.

To find:

The distance of the plane from the base of the cone.

Solution:

We draw the attached figure. (Check the picture)

Let the radius of the cross section be r cm.

Then the area of the cross section is πr² cm square.

Given, πr² = 154

or, 22/7 × r² = 154

or, r² = 7/22 × 154

or, r² = 7 × 7

or, r² = 7²

or, r = 7

So, the radius of the cross section is 7 cm.

Let the distance of the plane from the base is x cm.

Then we can draw two triangles ADE and ABC, which are similar triangles.

From the property of similar triangles, we can write:

AD / AB = DE / BC

or, (25 - x) / 25 = 7 / 10

or, 10 (25 - x) = 175

or, 250 - 10x = 175

or, 10x = 75

or, x = 7.5

Answer:

Therefore the distance of the plane from the base of the cone is 7.5 cm.

hope this helps you!!

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