Answer
Option E is correct.
Total surface area of the composite figure = 295.6 units²
Step-by-step explanation
The figure consists of a cone and a hemispherical bowl.
So, the surface area of the figure will be the sum of the curved surface area of the cone and the surface area of the hemispherical bowl.
Curved Surface of the cone = πrL
where
π = pi = 3.14
r = radius of the cone = 4 units
L = Curved slant height of the cone = ?
We are not given that from the question, but we are given the perpendicular height of the cone and its radius.
To obtain the curved slant height, we will use Pythagoras theorem.
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
From the right angle triangle in the cone,
a = 4
b = 15
hyp = L = ?
a² + b² = (hyp)²
4² + 15² = L²
16 + 225 = L²
L² = 241
Take the square root of both sides
√(L²) = √(241)
L = 15.524 units
Curved Surface of the cone = πrL
π = pi = (22/7)
r = radius = 4 units
L = Curved slant height = 15.524 units
Curved Surface of the cone = πrL
Curved Surface of the cone = (22/7) (4) (15.524) = 195.16 units²
Surface area of the hemispherical bowl = 2πr²
π = pi = (22/7)
r = radius of the hemispherical bowl = 4 units
Surface area of the hemispherical bowl = 2πr²
Surface area of the hemispherical bowl = 2 (22/7) (4²) = 100.57 units²
Total surface area of the composite figure
= (Curved Surface of the cone) + (Surface area of the hemispherical bowl)
= 195.16 + 100.57
= 295.73
= 295.6 units²
This is the closest value to the answer calculated.
Hope this Helps!!!