Question

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 canvas required (ans:-99.825 m2)​

Answer 1

Given:-

→ Diameter of the conical heap of

wheat = 10.5m

→ Height of the heap = 3m

To find:-

→ Volume of the conical heap.

→ Area of canvas required to protect the

heap from rain.

Solution:-

Firstly, let's calculate the radius of the heap :-

=> Radius = Diameter/2

=> Radius = 10.5/2

=> Radius = 5.25m

Volume of the conical heap :-

=> Volume of cone = 1/3πr²h

=> 1/3×22/7×(5.25)²×3

=> 22/7×5.25×5.25

=> 86.625 m³

Now, area of the canvas required will be equal to the Curved Surface Area of the conical heap of wheat.

=> C.S.A of the cone = πrl

=> πr×[√h² + r²] [ ∵ l = √h²+r² ]

=> 22/7×5.25×[√(3)²+(5.25)²]

=> 16.5×[√9+27.5625]

=> 16.5×[√36.5625]

=> 16.5×6.0466

=> 99.8m²

Thus:-

• Volume of the conical heap of wheat

is 86.625m³ .

• Area of canvas required is 99.8m² .

Answer 2

1. Radius = 5.25 m
2. Height = 3 m

• Volume = πr²h/3

V = 22/7 × 5.25² × 3/3

Volume = 86.25 m³

• Area=πrl

l=√h²+r² = √3²+5.25² = 6.046 m

A = 22/7 × 5.25 × 6.046

Area = 99.759 m²