Advertisements
Advertisements
Question
A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. [Use`pi22/7` ]
Solution
Let the height of the bucket be h cm.
Suppose r1 and r2 be the radii of the circular ends of the bucket.
Given, r1 = 28 cm and r2 = 21 cm
Capacity of bucket = 28.49 litres
∴Volume of the bucket = 28.49 × 1000 cm3 [1 litre = 1000 cm3]
`rArr1/3pih(r_1^2+r_2^2+r_1r_2)=28.49xx1000cm^3`
`rArr1/3xx22/7xxhxx[(28)^2+(21)^2+(28xx21)]cm^2=28490`
`rArr22/21xxhxx1813=28490 cm`
`rArrh=(28940x21)/(22xx1813)cm`
`h=15cm`
Thus, the height of the bucket is 15 cm.
RELATED QUESTIONS
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flagstaff are respectively 60° and 45°. Find the height of the flag-staff and that of the tower.
A man sitting at a height of 20 m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with the foot of the tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60° and 30°respectively. Find the width of the river.
The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
A lift in a building of height 90 feet with transparent glass walls is descending from the top of the building. At the top of the building, the angle of depression to a fountain in the garden is 60°. Two minutes later, the angle of depression reduces to 30°. If the fountain is `30sqrt(3)` feet from the entrance of the lift, find the speed of the lift which is descending.
A tower stands vertically on the ground. From a point on the ground, which is 30 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 30°. Find the height of the tower.
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 shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower.
If one looks from a tower 10 m high at the top of a flag staff, the depression angle of 30° is made. Also, looking at the bottom of the staff from the tower, the angle of the depression made is of 60°. Find the height of the flag staff.
From the top of building AB, a point C is observed on the ground whose angle of depression is 60° and which is at a distance of 40 m from the base of the building. Complete the following activity to find the height of building AB.
From figure, BC = `square`, ∠ACB = `square`
In ΔACB,
tan `square = square/(BC)`
⇒ `square = square/square`
⇒ `square = square`
Hence, the height of the building AB is `square`.
Find the length of the shadow on the ground of a pole of height 18m when angle of elevation θ of the sun is such that tan θ = `6/7`.
