A tall cylindrical reservoir kept vertically is 20 m in diameter. Water is poured into it at the rate of 264 m³ per hour. What is the rate at which the water level rises in the reservoir per minute? (Take π = 22/7)
1.4 cm
Rate of inflow = \(264\ \text{m}^3/\text{hr} = 4.4\ \text{m}^3/\text{min}\). Base area of reservoir (radius 10 m) = \(\pi r^2 = \frac{22}{7}\times 100 = \frac{2200}{7}\ \text{m}^2\). Rate of rise = \(\frac{4.4}{2200/7} = \frac{4.4 \times 7}{2200} = 0.014\ \text{m/min} = 1.4\ \text{cm/min}\).
A reservoir is in the form of a cuboid. Its length is 30 m. If 24 kL of water is removed from the reservoir, the water level goes down by 20 cm. What is the width of the reservoir?
A thin metallic sheet, 1.92 m² in area, is cut into two equal pieces. One piece is used to make a hollow cube of volume P (in m³) and the other is used to make a hollow cuboid of volume Q (in m³) with dimensions in the ratio \(4:2:1\). If no sheet is wasted, which one of the following is correct?
How many square metres of canvas (approximately) will be required to make a conical tent 3 m high so that a man 2 m tall may stand anywhere within a radius of 1 m from its centre without stooping?
A room is L m long, B m wide and H m high. Further, L > B > H and L, B and H are integers. The length of the longest pole that can be placed in the room is 17 m and the length of the longest pole that can be placed on the floor is 15 m. What is the volume of the room?
N number of cubes each of side length equal to 10 cm are joined end to end in a row. If the total surface area of the resulting cuboid is \(3800\text{ cm}^2\), then what is the value of N?
A spherical metal ball is molten and made into n smaller identical spheres. In this process, the surface area of the smaller balls increases by 900%. What is the value of n?
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)