Exercise 13.1 of class 9 NCERT math text book comprises 8 questions. This exercise focuses on Surface area of cube and cuboid and the lateral surface area of cube and lateral surface area of rectangular cuboid. Detailed explanation has been provided for all 8 questions. Video solution has been provided for questions 3, 6, and 7.
The formula to compute the surface area of cube is 6a^{2}, where 'a' is the edge of the cube.
The formula to compute the surface area of cuboid is 2(lb + bh + hl), where 'l, b, and h' are the three edges of the cuboid.
The formula to compute the lateral surface area of cube is 4a^{2}, where 'a' is the edge of the cube.
The formula to compute lateral surface area of cuboid is 2(lh + bh) = 2(l + b)h, where 'l, b, and h' are the three edges of the cuboid.
The lateral surface area of a cube or a cuboid is the product of the base perimeter and the height.
Question 1
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is open at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 m^{2} costs Rs 20.
Question 2
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs.7.50 per m^{2}.
Question 3
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs.10 per m^{2} is Rs.15000, find the height of the hall.
[Hint: Area of the four walls = Lateral surface area.]
Question 4
The paint in a certain container is sufficient to paint an area equal to 9.375 m^{2}. How many bricks of dimensions 22.5 cm x 10 cm x 7.5 cm can be painted out of this container?
Question 5
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
Question 6
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.
(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?
Question 7
Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm x 20 cm x 5 cm and the smaller of dimensions 15 cm x 12 cm x 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs.4 for 1000 cm^{2}, find the cost of cardboard required for supplying 250 boxes of each kind.
Question 8
Parveen wanted to make a temporary shelter for her car, by making a box-like structure, with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m x 3 m?
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