A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas.

Given

Radius (r) of heap = (10.5/2) m = 5.25

Height (h) of heap = 3m

Solution

Volume of cone = (1/3) × πr2h

On taking π=22/7

= (1/3) × (22/7) × (105/2) × (105/2) × 3

= (22 × 105 × 105 × 3) / (3 × 20× 20× 7)

V = 86.625 m3

Area of the canvas = surface area of cone = πrl

Slant height (l) = √(h+ r2)

l = √(3+ (10.5/2)2)

l = √(9+ (110.25/4))

l = √(146.25/4)

l = √36.56

l = 6.05 m (approx.) 

Surface area of cone = π × (105/20) × 6.05 m2

On taking π=22/7

= (22/7) × (635.25/20)

= 99.82 m2

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