The total surface area of a cone is equal to the sum of the lateral surface area ((π)(r)(s){\displaystyle (\pi )(r)(s)}) and the base area ((π)(r2){\displaystyle (\pi )(r^{2})}), since the base of a cone is a circle. The slant height is the diagonal distance from the top vertex of the cone to the edge of the base. [2] X Research source Make sure you don’t confuse the “slant height” with the “height,” which is the perpendicular distance between the top vertex to the base. [3] X Research source
For example, if the radius of the base of a cone is 5 cm, your formula will look like this: SA=(π)(5)(s)+(π)(52){\displaystyle {\text{SA}}=(\pi )(5)(s)+(\pi )(5^{2})}.
For example, if the slant height of a cone is 10 cm, your formula will look like this: SA=(π)(5)(10)+(π)(52){\displaystyle {\text{SA}}=(\pi )(5)(10)+(\pi )(5^{2})}.
For example:SA=(π)(5)(10)+(π)(52){\displaystyle {\text{SA}}=(\pi )(5)(10)+(\pi )(5^{2})}SA=(3. 14)(5)(10)+(π)(52){\displaystyle {\text{SA}}=(3. 14)(5)(10)+(\pi )(5^{2})}SA=157+(π)(52){\displaystyle {\text{SA}}=157+(\pi )(5^{2})}
For example:SA=157+(π)(52){\displaystyle {\text{SA}}=157+(\pi )(5^{2})}SA=157+(3. 14)(25){\displaystyle {\text{SA}}=157+(3. 14)(25)}SA=157+78. 5{\displaystyle {\text{SA}}=157+78. 5}
For example:SA=157+78. 5=235. 5{\displaystyle {\text{SA}}=157+78. 5=235. 5}So, the surface area of a cone with a radius of 5 cm and a slant height of 10 cm is 235. 5 square centimeters.
Make sure you don’t confuse the height of the cone with the slant height, which is the diagonal distance from the top vertex of the cone to the edge of the base. [7] X Research source The height is the perpendicular distance between the top vertex to the base. [8] X Research source
For example, if the radius of a cone is 5 cm and the height is 12 cm, your formula will look like this: 52+122=c2{\displaystyle 5^{2}+12^{2}=c^{2}}.
For example:52+122=c2{\displaystyle 5^{2}+12^{2}=c^{2}}25+144=c2{\displaystyle 25+144=c^{2}}169=c2{\displaystyle 169=c^{2}}
For example:169=c2{\displaystyle 169=c^{2}}169=c2{\displaystyle {\sqrt {169}}={\sqrt {c^{2}}}}13=c{\displaystyle 13=c}So, the slant height of the cone is 13 cm.
The total surface area of a cone is equal to the sum of the lateral surface area ((π)(r)(s){\displaystyle (\pi )(r)(s)}) and the base area ((π)(r2){\displaystyle (\pi )(r^{2})}, since the base of a cone is a circle).
For example, for a cone with a radius of 5 cm and a slant height of 13 cm, your formula will look like this: SA=(3. 14)(5)(13)+(3. 14)(52){\displaystyle {\text{SA}}=(3. 14)(5)(13)+(3. 14)(5^{2})}.
For example:SA=(3. 14)(5)(13)+(3. 14)(52){\displaystyle {\text{SA}}=(3. 14)(5)(13)+(3. 14)(5^{2})}SA=204. 1+(3. 14)(25){\displaystyle {\text{SA}}=204. 1+(3. 14)(25)}SA=204. 1+78. 5{\displaystyle {\text{SA}}=204. 1+78. 5}SA=282. 6{\displaystyle {\text{SA}}=282. 6}So, the surface area of a cone with a radius of 5 cm and a height of 12 cm is 282. 6 square centimeters.
Make sure you don’t confuse the height of the cone with the slant height, which is the diagonal distance from the top vertex of the cone to the edge of the base. [13] X Research source The height is the perpendicular distance between the top vertex to the base. [14] X Research source
For example, if you know a cone has a volume of 950 cubic centimeters and a radius of 6 centimeters, your formula will look like this: 950=13(3. 14)(62)(h){\displaystyle 950={\frac {1}{3}}(3. 14)(6^{2})(h)}.
For example:950=13(3. 14)(62)(h){\displaystyle 950={\frac {1}{3}}(3. 14)(6^{2})(h)}950=13(3. 14)(36)(h){\displaystyle 950={\frac {1}{3}}(3. 14)(36)(h)}950=13(113. 04)(h){\displaystyle 950={\frac {1}{3}}(113. 04)(h)}950=37. 68h{\displaystyle 950=37. 68h}
For example:950=37. 68h{\displaystyle 950=37. 68h}95037. 68=37. 68h37. 68{\displaystyle {\frac {950}{37. 68}}={\frac {37. 68h}{37. 68}}}25. 21=h{\displaystyle 25. 21=h}So, the height of the cone is 25. 21 cm.
For example, if the radius of a cone is 6 cm and the height is 25. 21 cm, your formula will look like this: 62+25. 212=c2{\displaystyle 6^{2}+25. 21^{2}=c^{2}}.
For example:62+25. 212=c2{\displaystyle 6^{2}+25. 21^{2}=c^{2}}36+635. 54=c2{\displaystyle 36+635. 54=c^{2}}671. 54=c2{\displaystyle 671. 54=c^{2}}671. 54=c2{\displaystyle {\sqrt {671. 54}}={\sqrt {c^{2}}}}25. 91=c{\displaystyle 25. 91=c}So, the slant height of the cone is 25. 91 cm.
The total surface area of a cone is equal to the sum of the lateral surface area ((π)(r)(s){\displaystyle (\pi )(r)(s)}) and the base area ((π)(r2){\displaystyle (\pi )(r^{2})}, since the base of a cone is a circle).
For example, for a cone with a radius of 6 cm and a slant height of 25. 91 cm, your formula will look like this: SA=(3. 14)(6)(25. 91)+(3. 14)(62){\displaystyle {\text{SA}}=(3. 14)(6)(25. 91)+(3. 14)(6^{2})}.
For example:SA=(3. 14)(6)(25. 91)+(3. 14)(62){\displaystyle {\text{SA}}=(3. 14)(6)(25. 91)+(3. 14)(6^{2})}SA=488. 14+(3. 14)(36){\displaystyle {\text{SA}}=488. 14+(3. 14)(36)}SA=488. 14+113. 04{\displaystyle {\text{SA}}=488. 14+113. 04}SA=601. 18{\displaystyle {\text{SA}}=601. 18}So, the surface area of a cone with a radius of 6 centimeters and a volume of 950 cubic centimeters is 601. 18 square centimeters.
