Advertisements
Advertisements
प्रश्न
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.
उत्तर
Radius of pipe = `7/2` cm
Rate of water flow = 36 km/h
= `36 xx 5/18` m/s
= 10 m/s
= 10 x 100 cm/s
= 1000 cm/s
∴ Volume of water flowing in 1 second = πr2h
= `π xx 7/2 xx 7/2 xx 1000` cm3
= π x 7 x 7 x 250 cm3 ....(1)
Radius of tank (R) = 35 cm
Height of tank (H) = 1 m = 100 cm
∴ Volume of tank = πr2H
= π x 35 x 35 x 100 cm3 ...(2)
∴ Time taken to fill the tank = `"Volume of tank"/"Volume of water flowing in 1 second"`
= `(π xx 35 xx 35 xx 100)/(π xx 7 xx 7 xx 250)` seconds
= 10 seconds
= `10/60` minute
= `1/6` minute.
APPEARS IN
संबंधित प्रश्न
Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm2. If this water is collected into a rectangular cistern of dimensions 7.5 m by 5 m by 4 m; calculate the rise in level in the cistern in 1 hour 15 minutes.
How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m in diameter ? Also, find the cost of plastering its inner surface at Rs 4.50 per sq meter.
How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?
Find the volume of the cylinder if the circumference of the cylinder is 132 cm and height is 25 cm.
A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.
A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate: the total area of the internal surface, excluding the base.
The diameter of the cross-section of a water pipe is 5 cm. Water flows through it at 10km/hr into a cistern in the form of a cylinder. If the radius of the base of the cistern is 2.5 m, find the height to which the water will rise in the cistern in 24 minutes.
The volume of a cylinder becomes ______ the original volume if its radius becomes half of the original radius.
Radius of a cylinder is r and the height is h. Find the change in the volume if the height is doubled.
A solid metallic cylinder is cut into two identical halves along its height (as shown in the diagram). The diameter of the cylinder is 7 cm and the height is 10 cm.
Find:
- The total surface area (both the halves).
- The total cost of painting the two halves at the rate of ₹ 30 per cm2 `("Use" π = 22/7)`.
