Sagot :
Answer:
111 cm^2
Step-by-step explanation:
h = 11.4
d = 5 so r (radius) = 2.5
Surface Area of a Cone Formula: πr^2 + πrs
s represents the slant height of the cone, lets represent this with a drawing.
We have the values of h and r, but we don't have the value of s, meaning we have to find it. We can do this by using pythagorean theorem.
a^2 + b^2 = c^2
These three values can come together to create a right triangle which we can seperate from the rest of the diagram, now we can find s.
s = √(11.4^2 + 2.5^2) so s = 11.67
now that we have all of the pieces, we can plug back into the original surface area formula. πr^2 + πrs
π(2.5^2) + π(2.5)(11.67) = 111.29 cm^2 or 111 cm^2
The surface area of the solid cone requiring paint will be 111 square cm.
What is the surface area of a cone?
Let d be the diameter of the base circle, l be the slant height, and h be the height of the cone.
Then the lateral surface area of the cone will be
SA = πrl + πr²
Then the slant height is given as
l² = r² + h²
The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.
Then the radius of the base circle will be
r = 5 / 2
r = 2.5 cm
The length of the slant height will be
l² = 11.4² + 2.5²
l² = 136.21
l = 11.67
Then the surface area of the solid cone requiring paint will be
SA = π × 2.5 × 11.67 + π × 2.5²
SA = 29.18π + 6.25π
SA = 35.43π
SA = 111.3
SA ≈ 111 square cm
The surface area of the solid cone requiring paint will be 111 square cm.
More about the surface area of a cone link is given below.
https://brainly.com/question/23877107
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