Volume of Cone
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.
The area of the base of a right circular cone is | |||
| Right Option : C | |||
| View Explanation | |||
The base radii of two right circular cones of the same height are in the ratio 3:5. Find the ratio of their volumes. | |||
| Right Option : B | |||
| View Explanation | |||
A right circular cone is 3.6 m high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height. | |||
| Right Option : A | |||
| View Explanation | |||
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