A conical heap is formed when a farmer pours food grains on a ground. The slant height of the heap is 35 cm. The circumference of the base is 132 cm. What amount of tarpaulin is needed to cover the grains? Farmer goes to the orphanage and gives half of the food grains for the children living there. How many grains farmer donated?

Concept Used: Circumference of the base of the cone = 2πr

Curved Surface Area of cone = πrl

The volume of cone

Where r = radius of the cone, h = height of the cone, and l = slant height of the cone.

Given:

The slant height of the heap = 35 cm

The circumference of the base = 132 cm

Explanation:

Let us find the radius of the Heap first,

2πr = 132 cm

r

r

r = 21 cm

The amount of tarpaulin to cover the heap = Curved Surface Area of the cone = πrl

Now put the value of “r” and “l” we get,

The amount of tarpaulin to cover the heap

The amount of tarpaulin to cover the heap = 2310 cm²

Amount of food grains = Volume of food grains

Amount of food grains

Now we need to calculate the height of the cone.

h =

h =

h = 28 cm

Putting the value of “h” in the formula of volume of the cone we get,

Amount of food grains

Amount of food grains = 12936 cm³

Now half of the food grains are donated to the orphanage,

Amount of food grains donated

Amount of food grains = 6468 cm³

Hence, The amount of food grains donated are 6468 cm³.