Maths-
General
Easy
Question
Three cylinders each of height 16 cm and radius of base 4 cm are placed on a plane so that each cylinder touches the other two. What is the volume of the region enclosed between the three cylinders?
Hint:
If we look from the top and follow the diagram, we have to calculate the volume of the blue shaded region. Join the centres of the circles to form an equilateral triangle. We then find the area of the triangle then multiplying with the height of the cylinders, we get the volume of the region enclosed by the triangles. Then we subtract the three sectors other than the blue shaded one to get the volume of the asked region.
The correct answer is: 128(2√3 - π) cm².
Explanations:
Step 1 of 4:
The side (a) of the equilateral triangle is of length 2r = 8cm (since given radius of base, r = 4 cm). We know that area of an equilateral triangle 
, where a = 8
Therefore, area = 
Step 2 of 4:
There are three equal sectors included in this area, each with an angle of 60°.
Area of the three sectors = 
Step 3 of 4:
Area between the circles 
cm²
Step 4 of 4:
Volume between the cylinders = Area × height
cm²
Final Answer:
the volume of the region enclosed between the three cylinders is 
cm².
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