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. Â
The cross section is given in Figure 1. Â
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
