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Question:

A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Solution:

Given that
A heap of rice is in the form of a cone
Diameter = d = 24 m
Radius = r = d/2 = 12 m
Height = h = 3.5 m
Volume of Cone = V = πr²h/3
V = (22/7) × 12² × 3.5 / 3 m³
V = (22/7) × 144 × 3.5 / 3 m³
V = 528 m³

Given that canvas cloth is required to just cover the heap
It covered the only curved surface area of Cone
Slant Height of cone = l = √h² + r²
l = √3.5² + 12² m
l = √12.25 + 144 m
l = √156.25 m
l = 12.5 m
Curved surface area of Cone S = πrl
S = (22/7) × 12 × 12.5 m²
S = 471.42 m²