Answer:
4677 Square Centimeters
Step-by-step explanation:
Diameter of the Triangle =10cm, therefore:
Radius of the triangle =5cm
The Cylindrical containers are enclosed in Triangular prisms where the triangular face is assumed to be an Equilateral Triangle.
The cross section is given in Figure 1.
In the Equilateral Triangle ABC, points P, Q and R are the points of tangency.
We apply the following theorems:
Theorem 1: The angle between a tangent and a radius is 90 degrees
Theorem 2: Tangents to a circle from the same point are equal.
In Right Triangle BPO, presented in Figure 2, From Figure 1, |BO| divides the angle at B into two equal parts of 30 degrees each since it is an equilateral triangle.
Therefore, Angle PBO=30 degrees.
Sin 30 =|PO|/|BO|
0.5=5/BO|
BO|=5/0.5=10cm
Similarly
Tan 30=5/|PB|
|PB|=5/Tan 30=5√3 cm
By the same process,
|AR|=5√3 cm
Theorem: The altitude of an equilateral triangle divides the base into two equal parts.
Therefore: |AR|=|RC|=5√3 cm
Height of the Triangle |BR|=|BO|+|OR|=10+5=15cm
Base of the Triangle, |AC| =5√3+5√3=10√3 cm
Area of the Triangle =0.5*15*10√3 =75√3 Square cm
The Prism has two equilateral triangular faces and three rectangular faces of the same dimension. See Figure 4.
Therefore:
Surface Area of the Triangular Prism=Area of Two Triangular Faces+Area of Three Rectangular Faces
=2(75√3)+3(10√3*85)
=4676.5 Square Centimeters
=4677 Square Centimeters
