A well is dug with a diameter of 3.5 m and 16 m depth. The earth soil so excavated is spread in the form of a right circular cone of radius 7 m. What is the height of the cone?
3 m
Radius of well = \(1.75\ \text{m}\). Volume of earth dug out = \(\pi r^2 h = \pi (1.75)^2 (16) = 49\pi\ \text{m}^3\). This is spread into a cone of radius 7 m and height H: \(\frac{1}{3}\pi (7)^2 H = 49\pi\), so \(\frac{49}{3}H = 49 \Rightarrow H = 3\ \text{m}\).
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 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)
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?
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 $\pi = \frac{22}{7}$)