Advertisements
Advertisements
Question
The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.
Solution
We have the following situation as shown in the figure
Let VAB be a cone of height h1 = VO1 =20cm. Then from the symmetric triangles VO 1A and VOA1, we have
`(VO_1)/(VO)=(O_1A)/(OA_1)`
⇒`20/(VO)=(O_1A)/(OA_1)`
It is given that, volume of the cone VA1O is`1/125`times the volume of the cone VAB. Hence, we have
`1/3piOA_1^2xxVO=1/125xx1/3piO_1A^2xx20`
⇒`((OA_1)/(O_1A))^2xxVO=4/25`
⇒`((VO)/20)^2xxVO=4/25`
⇒`VO^3=(400xx4)/25`
⇒ VO3 = 16 x 4
⇒ VO = 4
Hence, the height at which the section is made is 20 − 4 = 16 cm.
APPEARS IN
RELATED QUESTIONS
A cylindrical jar of radius 6cm contains oil. Iron sphere each of radius 1.5cm are immersed in the oil. How many spheres are necessary to raise level of the oil by two centimetress?
A vessel in the shape of cuboid ontains some water. If these identical spheres are immersed in the water, the level of water is increased by 2cm. if the area of base of cuboid is 160cm2 and its height 12cm, determine radius of any of spheres?
A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm. Determine the capacity of the tank.
The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m2. If the pipe is made of 99 cm3 of metal, find the outer and inner radii of the pipe.
The radii of two cylinders are in the ratio 3 : 5. If their heights are in the ratio 2 : 3, then the ratio of their curved surface areas is
Choose the correct answer of the following question:
The number of solid spheres, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is
A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm. Find the rise in the level of water.
Given that 1 cu. cm of marble weighs 25 g, the weight of a marble block of 28 cm in width and 5 cm thick, is 112 kg. The length of the block is ______.
A surahi is the combination of ______.
A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains `41 19/21 m^3` of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?
