CBSE Class 10 Mathematics Surface Area and Volume Assignment Set 14

Question. The edge of a Cubical room is \( 8\text{ m} \). Find its total S.A. Also find the number of students it can accommodate if each student requires \( 2.56\text{ cu.m.} \) of space.
Answer: \( \text{S.A.} = 384\text{ m}^2 \), \( \text{No. of Students} = 200 \)

Question. Three cubes whose edges measures \( 3\text{ cm} \), \( 4\text{ cm} \) and \( 5\text{ cm} \) respectively are melted to form a single cube. Find the Surface of the new cube, supposing that there is no waste in the process.
Answer: \( 216\text{ cm}^2 \)

Question. A rectangular water reservoir measures \( 8\text{ m} \) by \( 4.5\text{ m} \) at the base. Water flows into it through a pipe whose cross-section is \( 5\text{ cm} \) by \( 3\text{ cm} \) at the rate of \( 10\text{ m} \) per second. Find the height to which the water will rise in the reservoir in \( 40 \) minutes.
Answer: \( 1\text{ m} \)

Question. Find the length of the longest rod that can be placed in a room \( 12\text{ m} \) long, \( 9\text{ m} \) broad and \( 8\text{ m} \) high.
Answer: \( 17\text{ m} \)

Question. In a shower \( 5\text{ cm} \) of rain falls. How many litres of water falls on \( 10 \) hectares of ground, supposing \( 1\text{ litre} = 1000\text{ c.c.} \)
Answer: \( 5 \times 10^6\text{ litres} \)

Question. How many bricks, measuring \( 25\text{ cm} \times 12\text{ cm} \times 8\text{ cm} \) will be required to construct a wall \( 10\text{ m} \) long, \( 4\text{ dm} \) wide and \( 3\text{ m} \) high?
Answer: \( 5000\text{ bricks} \)

Question. The length of the diagonal of a cube is \( 6\text{ m} \). What is the Solid Content?
Answer: \( 24\sqrt{3}\text{ m}^3 \)

Question. A School room is to be built to accommodate \( 150 \) children, so as to allow \( 2.5\text{ sq.m.} \) of floor area and \( 20\text{ cu.m.} \) of space for each child. If the room be \( 15\text{ m} \) broad, what must be its length and height?
Answer: \( l = 25\text{ m} \), \( h = 8\text{ m} \)

Question. The Surface of a Cube is \( 384\text{ cm}^2 \). Find its Volume
Answer: \( 512\text{ cm}^3 \)

Question. The areas of three faces of a rectangular block are in the ratio \( 2:3:4 \) and its Volume is \( 9000\text{ cu-cm.} \) Find the length of the shortest side.
Answer: \( 15\text{ cm.} \)