Advertisements
Advertisements
प्रश्न
The dimensions of a solid iron cuboid are 4·4 m × 2·6 m × 1·0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe
उत्तर
Let the length of the pipe be h cm.
Volume of the solid iron cuboid = 4·4 m × 2·6 m × 1·0 m = 440 cm×260 cm×100 cm
Internal radius of the pipe, r = 30 cm
External radius of the pipe, R = 30 + 5 = 35 cm
Volume of iron in the pipe = `piR^2h - pir^2h = pih(R^2 - r^2)`
`= pih(35^2 - 30^2)`
`= pih(35 - 30)(35 + 30)`
`= pih(5 xx 65)`
Volume of iron in the pipe = Volume solid iron cuboid
`=> pih(5 xx 65) = 440 xx 260 xx 100`
`=> h = (440 xx 260 xx 100 xx 7)/(5 xx 65 xx 22)`
`=> h = 11200 cm = 112m`
Hence, the length of the pipe is 112 m.
APPEARS IN
संबंधित प्रश्न
A right angled triangle whose sides are 3 cm, 4 cm and 5 cm is revolved about the sides containing the right angle in two days. Find the difference in columes of the two cones so formed. Also, find their curved surfaces.
A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm2 .
Find the surface area of a sphere of radius 7 cm.
A cubic cm of gold is drawn into a wire 0.1 mm in diameter, find the length of the wire.
A cylindrical vessel 32 cm high and 18 cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, the radius of its base is
The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is
A solid sphere of radius 3 cm is melted and then cast into small spherical balls, each of diameter 0.6 cm. Find the number of balls obtained.
In the above figure, a sphere is placed in a cylinder. It touches the top, bottom and curved surface of the cylinder. If the radius of the base of the cylinder is ‘r’, write the answer to the following questions.
a. What is the height of the cylinder in terms of ‘r’?
b. What is the ratio of the curved surface area of the cylinder and the surface area of the sphere?
c. What is the ratio of volumes of the cylinder and of the sphere?
______ surface area of room = area of 4 walls.
Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. Find the area left ungrazed by the horses.
