Advertisements
Advertisements
प्रश्न
The height and the radius of the base of a cylinder are in the ratio 3 : 1. If it volume is 1029 π cm3; find it total surface area.
उत्तर
Ratio between height and radius of a cylinder = 3 : 1
Volume = 1029 πcm3 ...(1)
Let radius of the base = r
Then height = 3r
∴ Volume = πr2h
= π × r2 × 3r
= 3πr3 ...(2)
From (1) and (2)
3πr3 = 1029π
`r^3 = 1029/3pi = 343`
r = 7
Therefore, radius = 7 cm and height = 3 × 7 = 21 cm
Now, total surface area = 2πr(h + r)
= `2 xx 22/7 xx 7 xx (21 + 7)`
= `2 xx 22/7 xx 7 xx 28`
= 1232 cm2
APPEARS IN
संबंधित प्रश्न
From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.
A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s–1. Calculate, in minutes, the time it takes to fill the tank.
A test tube consists of a hemisphere and a cylinder of the same radius. The volume of the water required to fill the whole tube is `5159/6 cm^3` and `4235/6 cm^3` of water is required to fill the tube to a level which is 4 cm below the top of the tube. Find the radius of the tube and the length of its cylindrical part.
A cylindrical container with internal radius of its base 10 cm, contains water up to a height of 7 cm. Find the area of the wet surface of the cylinder.
A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.
Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along its :
- shorter side.
- longer side.
The total surface area of a solid cylinder is 616 cm2. If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.
Water flows through a cylindrical pipe of internal diameter 7 cm at 36 km/hr. Calculate the time in minutes it would take to fill the cylindrical tank, the radius of whose base is 35 cm, and height is 1 m.
A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of radius 5 cm and height 4 cm is immersed it completely. Calculate the raise of the water in the glass?
A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, find how many litres of milk is needed to serve 1600 students.
