Surface area help I am struggling

Total Surface Area: 65.97 cm²

Lateral Surface Area: 37.70 cm²

Step-by-step 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.

sites:

one set of data has more variation than the other. hope this !