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?
9
N cubes of side 10 cm joined end to end form a cuboid of dimensions \(10\text{ cm} \times 10\text{ cm} \times 10N\text{ cm}\). Its total surface area is \(2(10\times10 + 10\times10N + 10\times10N) = 200 + 400N\). Setting this equal to \(3800\text{ cm}^2\) gives \(400N = 3600 \Rightarrow N = 9\).
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?
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 $\pi = \frac{22}{7}$)