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Why is this concept useful?: The Distance Formula is used to solve problems involving finding the distance between two points. Using this method provides a quicker way than using the Pythagorean Theorem as the Distance Formula is derived from it.
Where does this concept fit into the curriculum?: Grade 8, High School Algebra

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What is a Right Circular Cone?

A Right Circular Cone is where the axis of the cone is a line from the vertex of the cone to the midpoint of the circular base. In other words, the altitude or height (h) of the cone is perpendicular to the radius (r) of the circular base as seen in the diagram below:

How to use Right Circular Cone formulas for surface area and volume:

Surface Area:

Formula for curved surface area of a right circular cone = πrl where r is the radius of circular base and l is the slant height of the cone

Total surface area formula of a right circular cone = surface area of circular base + surface area of curved surface =

\pi r^{2} +\pi rl

To find the l (slant height) of the cone, the slant height is the hypotenuse of the right triangle formed between the radius and height of the circular cone

where

l=\sqrt{r^{2} +h^{2}}

To find the volume of a right circular cone the following formula is used:

v_{cone} =\frac{\pi r^{2} h}{3}

Sample Math Problems

1. Find the volume of a cone with a height of 10 inches and radius of 1 inch

Solution:

v_{cone} =\frac{\pi r^{2} h}{3} =\frac{\pi 1^{2} 10}{3} =\frac{10\pi }{3} =around\ 10.47\ in^{2}

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Practice Math Problems

1. Find the volume of a cone with radius 4 cm and height 10 cm

2. Find the volume of a cone with radius 3 cm and slant height 5 cm

3. What is the total surface area of a cone that has a radius of 3 m and a height of 10 m

4. What is the curved surface area of a cone that has a radius of 3 m and a height of 10 m

2. Find the volume of a cone with a height of 5 inches and radius of 2 inches

Solution:

v_{cone} =\frac{\pi r^{2} h}{3} =\frac{\pi 2^{2} 5}{3} =\frac{20\pi }{3} =around\ 20.84\ in^{2}

3. What is the curved surface area of a cone that has a radius of 3 m and a height of 4 m?

Solution:

First we have to find l.

l=\sqrt{r^{2} +h^{2}} \ =\ \sqrt{3^{2} +4^{2}} =\sqrt{25} =5

Then we have to use the curved surface area formula to find the area: Curved surface area = πrl= π(3)(5)=15π meters sq.

4. What is the total surface area of a cone that has a radius of 3 m and a slant height of 5 m?

Solution:

Using the total surface area formula

Total surface area=

Total\ surface\ area=\pi r^{2} +\pi rl=\ \pi ( r+l) =3\pi ( 3+5) =24\pi \ meters\ sq.

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Geometry Worksheets

Right Circular Cone

Related Topics

Normal Distribution

Tossing a Coin

Properties of Exponents

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