Volume of Cone

Cone: A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex.

Volume of Cone: .The volume V of a cone with radius r is one-third the area of the base B times the height h.

Volume of the cone of radius r and height h =

Illustration: Find the volume of a right circular cone 1.02m high , if the radius of its base is 28 cm.

Solution: We know that the volume V of a right circular cone of radius r and height h is given .   Here,   r = 28cm   and h = 1.02 m = 1.02 X 100 cm = 102 cm

Illustration: A conical tent is 9 m high and the radius of its base is 12 m.

(i) What is the cost of the canvas required to make it, if a square metre canvas costs Rs 10?

(ii) How many persons can be accommodated in the tent, if each person requires 2 square metre on the ground and of space to breath in?

Solution: We have,

r = Radius of the base of the conical tent = 12 m

h = Height of the conical tent = 9 m

l = Slant height of the conical tent =

(i) Area of the lateral surface =

So, total cost of the canvas = Rs(565.2 X 10) = Rs 5652

(ii) Area of the base of the conical tent =

As each person requires 2 sq. metres of floor area.

So, max number of persons who will have enough space on the ground

Also, Volume of the conical tent

Volume of the conical tent

Volume of the conical tent = 1356.48

We have, air space required person

So, number of persons who will have enough air space to breath in

Between 226 and 90, the smaller number is 90.

Hence 90 persons can be accomodated.