High Impact Tutoring Built By Math Experts
Personalized standards-aligned one-on-one math tutoring for schools and districts
In order to access this I need to be confident with:
Area of a circle Right triangle Right angle HypotenuseHere you will learn about the surface area of a cone, including how to find the surface area given the radius of a cone and the slant height.
Students will first learn about the surface area of a cone as a part of geometry in katex is not definedth grade.
The surface area of a cone is the area which covers the outer surface of the cone.
For any cone, katex is not defined is the radius of the base of the cone, katex is not defined is the slant height of the cone, and katex is not defined is the perpendicular height of the cone.
In order to calculate the total surface area of a cone (tsa), find the area of the two parts of the surface of the cone and add them together.
There is a curved surface area (CSA) and a circular base. The curved surface area of a cone is sometimes referred to as the lateral surface area of a cone (lsa).
The surface area of a cone is the area of the two parts added together:
katex is not defined
The perpendicular height of a cone katex is not defined is not required to calculate the surface area of a cone, although it is used to calculate the volume of the cone.
Step by step guide: Volume of a cone
Note: You cannot use the formula for the surface area of a cone written above for an oblique cone. This is because the curved surface area does not have a constant slant height katex is not defined from the apex (a vertex) to the circular base.
Example
Calculate the surface area of the cone below to katex is not defined decimal place.
Add these together to find the total surface area of the cone:
katex is not definedHow does this relate to katex is not definedth grade math?
Use this quiz to check your grade 6 students’ understanding of surface area. 10+ questions with answers covering a range of 6th grade surface area topics to identify areas of strength and support!
DOWNLOAD FREEUse this quiz to check your grade 6 students’ understanding of surface area. 10+ questions with answers covering a range of 6th grade surface area topics to identify areas of strength and support!
DOWNLOAD FREEIn order to calculate the surface area of a cone:
Find the curved surface area of the cone below. The radius of the cone is katex is not defined and the slant height is katex is not defined Write your answer to katex is not defined decimal place.
You will only calculate the area of the curved surface for this question.
katex is not defined2Add the areas together.
Because you are calculating the area of the curved surface, you can move on to step 3.
3Write the answer, including the units.
Round the answer to katex is not defined decimal place and include the units.
katex is not definedThe curved surface area of the cone is katex is not defined
Note: If the question asks for katex is not defined decimal place, the answer must have katex is not defined decimal place, even if the digit is katex is not defined
Find the total surface area of the cone below to katex is not defined decimal place.
Find the area of each face.
Add the areas together.
The sum of the areas is:
katex is not defined
Write the answer, including the units.
Write the answer to katex is not defined decimal place and with square units.
katex is not defined
The total surface area of the cone is katex is not defined
A chip shop sells mushy peas in a conical pot. The lid has a radius of katex is not defined and the pot has a slant height of katex is not defined Calculate the outside surface area of the closed pot, including the lid. Write your answer in terms of katex is not defined
Find the area of each face.
Add the areas together.
The sum of the areas is katex is not defined
Write the answer, including the units.
Write the answer in terms of katex is not defined and state the units.
The total surface area of the cone is: katex is not defined
The roof of a tower is a solid cone. The radius of the circular base is katex is not defined and the roof has a slope length of katex is not defined Calculate the surface area of the roof. Write your answer in the form katex is not defined where katex is not defined and katex is not defined are integers with no common factors.
Find the area of each face.
Add the areas together.
The sum of the areas is equal to:
katex is not defined
Write the answer, including the units.
The answer needs to be written in the form katex is not defined where katex is not defined and katex is not defined are integers with no common factors. By simplifying the fraction fully, you get katex is not defined
The surface area of the solid cone is katex is not defined
Calculate the surface area of a cone with a base diameter of katex is not defined and a slant height of katex is not defined Give your answer to katex is not defined significant figures.
Find the area of each face.
Calculate the radius of the circular base first. As the diameter is twice the radius of a circle, divide the diameter of the circle by katex is not defined
katex is not defined
You are left with katex is not defined
Add the areas together.
Add the two areas together.
katex is not defined
Write the answer, including the units.
Write the answer to katex is not defined significant figures, and state the units.
katex is not defined
The surface area of the cone is katex is not defined
A cone has a perpendicular height of katex is not defined and a circular base with a radius of katex is not defined The apex of the cone is directly above the center of the circular base. Calculate the area of the curved surface in terms of katex is not defined
Find the area of each face.
Find the slant height of the cone. Sketching a diagram of the cone with the dimensions given:
To find the slant height of a cone, katex is not defined use Pythagoras’ theorem:
katex is not defined
Given that katex is not defined and katex is not defined you have:
With the value for the slant height, you can find the curved surface area.
Add the areas together.
Because you are calculating the area of the curved surface, you can move on to step katex is not defined
Write the answer, including the units.
Leave the answer in terms of katex is not defined and include the units.
The curved surface area of the cone is katex is not defined
1. Find the curved surface area of a cone of radius katex is not defined and slant height katex is not defined Give your answer to katex is not defined significant figures.
To find the curved surface area of a cone, substitute the value of katex is not defined and katex is not defined into the formula.
katex is not defined
2. A cone has a radius of katex is not defined and a slant height of katex is not defined Calculate the curved surface area of the cone, to katex is not defined significant figures.
To find the curved surface area of a cone, substitute the value of katex is not defined and katex is not defined into the formula.
katex is not defined
3. A candle is made in the shape of a cone. The radius of the base is katex is not defined and the slant height is katex is not defined Calculate the surface area of the candle to katex is not defined decimal place.
To find the total surface area of a cone, find the curved surface area and add on the area of the circular base.
katex is not defined
katex is not defined
Total surface area: katex is not defined
katex is not defined
4. Find the total surface area of a cone of radius katex is not defined and slant height katex is not defined Write your answer as a fraction in the form katex is not defined where katex is not defined and katex is not defined are integers. State the units in your answer.
To find the total surface area of a cone, find the curved surface area and add on the area of the circular base.
katex is not defined
katex is not defined
Total surface area:
katex is not defined
Surface area is equal to katex is not defined
5. A conical party hat has a diameter of katex is not defined and a slant height of katex is not defined An image is being placed on the entire outside surface of the party hat. What is the area of the image? Write your answer in terms of katex is not defined
The diameter is twice the length of the radius and so katex is not defined
Substituting the values for katex is not defined and katex is not defined into the formula for the curved surface area you get,
katex is not defined
6. A cone has a radius of katex is not defined and a perpendicular height of katex is not defined The apex of the cone is directly above the center of the circular base. Calculate the surface area of the cone to katex is not defined significant figures.
Use Pythagoras’ theorem to calculate the slant height of the cone, then determine the surface area.
Pythagoras’ theorem: katex is not defined
katex is not defined
The slant height katex is not defined
katex is not defined
katex is not defined
Total surface area: katex is not defined
The total surface area of the cone is katex is not defined
A cone is a 3D geometric shape that tapers from a flat base to a point called the apex. The base of a cone is typically a circle, but not always.
Finding the surface area of a right circular cone is the same as finding the surface area of any cone. You will first find the area of the curved surface using the formula katex is not defined You will add the answer of the area of the curved surface to the area of the base, using the formula katex is not defined
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.
Find out how we can help your students achieve success with our math tutoring programs.
Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!
Notifications