Answer:
Total Surface Area: 65.97 cm²
Lateral Surface Area: 37.70 cm²
Explanation:
You can solve for the surface area without the height or you can solve for the height and then find the surface are, either way is easy.
Lets first solve without the height. We will solve the surface area with the radius and slant height.
Total Surface area of cone formula: πr (r + s)
Curved surface are formula: πrs
Substitute the values in the picture with the formula
Slant height: 4
Radius: 3
πr (r + s)
π(3)(3 + 4)
(3.141593)(3)(3 + 4)
=9.424778(3 + 4)
=(9.424778)(7)
=65.973446
65.973446 rounded to the nearest hundredth is 65.97
TSA = Total Surface Area
TSA = 65.97 cm²
Now to find the curved surface area or some people call it the Lateral Surface Area
Formula: πrs
Radius: 3
Slant Height: 4
π(3)(4)
(3.141593)(3)(4)
=(9.424778)(4)
=37.699112
37.699112 to the nearest hundredth is 37.70
CSA = Curved Surface Area
CSA = 37.70 cm²
If you choose to compute the height (h) the you have to know both the radius (r) and the slant height (s):
Formula: height (h) = √s² - r²
Slant height = s = 4
Radius = r = 3
Height = h = ?
Now substitute the values into the formula
h = √s² - r²
h = √4² - 3²
h = √16 - 9
h = √7
h = 2.64575131
Height: 2.64575131 cm
Now it's time to find the surface area and curved surface area, now that you have the height:
Surface area formula given height and radius: πr(r + √(r² + h²))
Substitute the values
Height: 2.64575131
Radius: 3
πr(r + √(r² + h²))
π(3)(3 + √(3² + 2.64575131²))
TSA = (3.141593)(3)(3 + √(3² + 2.64575131²)
TSA = 9.424778(3 + √(3² + 2.64575131²)
TSA = 9.424778(3 + √(9 + 7)
TSA = 9.424778(3 + √(16)
TSA = 9.424778(3 + 4)
TSA = 9.424778(7)
TSA = 65.973446
TSA = 65.97
Next, time to find the Curved surface area:
Formula: CSA = πr√(r² + h²)
CSA = πr√(r² + h²)
Substitute the values into the formula
Radius: 3
Height: 2.64575131
Slant Height: 4
CSA = πr√(r² + h²)
CSA = π(3)√(3² + 2.64575131²)
CSA = 9.424778√(3² + 2.64575131²)
CSA = 9.424778√(9 + 7)
CSA = 9.424778√(16)
CSA = 9.424778(4)
CSA = 37.699112
CSA = 37.70
So, we can conclude that the Total Surface Area is 65.97 and the Lateral Surface Area is 37.70.