Advertisements
Advertisements
Question
A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is
Options
A. 1 : 2
B. 1 : 4
C. 1 : 6
D. 1 : 8
Solution
Let the height and the radius of whole cone be H and R respectively.
The cone is divided into two parts by drawing a plane through the mid point of its height and parallel to the base.
Let the radius of the smaller cone be r cm.
In ∆OCD and ∆OAB,
∠OCD = ∠OAB (90°)
∠COD = ∠AOB (Common)
∴∆OCD ∼ ∆OAB (AA Similarity criterion)
⇒ R = 2r
Thus, the ratio of smaller cone to whole cone is 1 : 8.
APPEARS IN
RELATED QUESTIONS
A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Find the speed of flying of the bird.
`("Take"sqrt3=1.732)`
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. `(sqrt(3) = 1.732)`
The angles of elevation of the top of the rock from the top and foot of 100 m high tower are respectively 30° and 45°. The height of the rock is ____________.
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45°. What is the height of the tower?
A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top ____________.
The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point, 10 m vertically above the first, its angle of elevation is 45°. Find the height of the tower.
A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.
The angles of elevation of the bottom and the top of a flag fixed at the top of a 25 m high building are 30° and 60° respectively from a point on the ground. Find the height of the flag.
