Find the area of the curved surface of a cone whose base radius is 3cm and whose height is 4cm (π = 3.14)
Answer Details
To find the curved surface area of a cone, we need to use the formula:
`Curved Surface Area = πrs`
where `r` is the radius of the base of the cone and `s` is the slant height of the cone.
To find the slant height of the cone, we can use the Pythagorean theorem, which tells us that:
`h^2 + r^2 = s^2`
where `h` is the height of the cone.
Substituting `r = 3cm` and `h = 4cm`, we get:
`4^2 + 3^2 = s^2`
`16 + 9 = s^2`
`25 = s^2`
`sqrt(25) = s`
`s = 5cm`
Now, substituting `r = 3cm` and `s = 5cm` into the formula for curved surface area, we get:
`Curved Surface Area = πrs`
`= 3.14 × 3 × 5`
`= 47.1cm^2`
Therefore, the curved surface area of the cone is `47.1cm^2`. Hence, option C, "47.1cm^2" is the correct answer.