Cone Quiz

Cone Quiz brings you closer to the fascinating geometry of cones, a shape that’s more common than you might think. Did you know that the Great Pyramid of Giza, when visualized in three dimensions, can be imagined as a series of stacked cones? The ancient Egyptians used precise geometric calculations to ensure its slant height and volume were perfect for its towering structure. Cones are not just mathematical shapes; they are deeply connected to architecture, design, and even nature. Understanding their volume, slant height, and lateral surface area can unlock insights into structures we admire every day. Test your understanding of these principles with challenging cone problems and discover the hidden mathematics behind one of the most elegant geometric shapes.

Cone

If the radius of a cone is doubled while its height remains constant, by what factor does its volume increase?

A cone is melted and recast into smaller cones of half the height and half the radius of the original. How many smaller cones are formed?

1/8

1/4

1/16

If the slant height of a cone is twice its radius, what is the ratio of its height to its radius?

1 : 3

3 : 1

1 : √3

√3 : 1

If a cone is cut by a plane parallel to its base, which of the following best describes the upper part?

A hemisphere

A smaller cone

A frustum

A cylinder

A cone has a volume of 54π cm³. If its radius is 3 cm, what is its height?

If the slant height of a cone is increased by 20%, while the radius remains constant, what happens to the lateral surface area?

Increases by 1.2%

Increases by 20%

Increases by 120%

Increases by 12%

If the lateral surface area of a cone is equal to its base area, what is the slant height in terms of the radius?

√3r

√2r

A cone is filled with water and then poured into another cone with twice the radius and twice the height. What fraction of the larger cone is filled?

A cone is sliced horizontally at half its height. What is the ratio of the volume of the smaller (top) cone to the original cone?

1/2

1/4

1/16

1/8

The height of a cone is twice its radius. If its radius is tripled, by what factor does its volume increase?

Your score is

The average score is 25%

Sample Questions from This Quiz

If the slant height of a cone is twice its radius, what is the ratio of its height to its radius?
If a cone is cut by a plane parallel to its base, which of the following best describes the upper part?
If the slant height of a cone is increased by 20%, while the radius remains constant, what happens to the lateral surface area?
A cone is filled with water and then poured into another cone with twice the radius and twice the height. What fraction of the larger cone is filled?
The height of a cone is twice its radius. If its radius is tripled, by what factor does its volume increase?

Try the full quiz and see how many of these you can answer!