Question:
What is the surface area of a cone using pi for 15cm for height and 3 cm for radius?
Answer:
The surface area of a cone = 172.1034 [tex]cm^2[/tex]
Step-by-step explanation:
Given:
Height of the cone = 15 cm
Radius of the cone = 3 cm
To Find:
Surface area of a cone =?
Solution:
The surface area of a cone
=> curved surface area + the area of the base
=>[tex]\pi r^2 + \pi L r[/tex] ------------------------------------------------(1)
where
r denotes the radius of the base of the cone, and
L denotes the slant height of the cone.
The curved surface area is also called the lateral area.
Let us first find the slant height:
[tex]L = \sqrt{r^2 +h^2}[/tex]
[tex]L = \sqrt{3^2 +15^2}[/tex]
[tex]L = \sqrt{9 +225}[/tex]
[tex]L = \sqrt{234}[/tex]
[tex]L =3 \sqrt{26}[/tex]
Substituting the values in (1)
=>[tex](\pi)( 3^2) + (\pi) (3\sqrt{26})(3)[/tex]
=>[tex](\pi)( 9) + (\pi) (3\sqrt{26})(3)[/tex]
=>[tex](3.14)( 9) + (3.14) (3\times 5.09})(3)[/tex]
=>[tex](3.14)( 9) + (3.14) (3\times 5.09})(3)[/tex]
=>[tex]( 28.26) + (3.14) (15.27)(3)[/tex]
=>[tex]( 28.26) + (143.8434)[/tex]
=> 172.1034
