Chapter 13 : Surface areas and volumes
Q. The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost white washing the walls of the room and ceiling at the rate of Rs. 7.50 per m2.
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Q. The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm×10 cm×7.5 cm can be painted out of this container?
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Q. 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 ×20 cm ×5 cm and the smaller of dimensions 15 cm ×12 cm ×5 cm. For all the overlaps, 5%of the total surface area is required extra. If the cost of the cardboard is 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.
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Q. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet,
(i) determine the area of the sheet
(ii) the cost of sheet for it, if a sheet measuring 1 m2 costs Rs.20.
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Q. 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 ×3 m?
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Q.

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 m2 is 15000, find the height of the hall (in meters).

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Q. A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.Which box has the greater lateral surface area and by how much?
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Q.

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25cm wide and 25cm high.
(i) What is the area of the glass?
(ii)
How much of tape is needed for all the 12 edges?

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Q. The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find
(i) its inner curved surface area
(ii) the cost of plastering the curved surface at the rate of Rs. 40 per m2
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Q. The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2
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Q. Find
(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.
(ii) How much steel was actually used, if 112 of the steel actually used was wasted in making the tank?
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Q. The curved surface area of a right circular cylinder of height 14cm is 88cm2. Find the diameter of the base of the cylinder.
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Q. In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
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Q. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m2.
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Q.

It is required to make a closed circular cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet is required for the same?

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Q.

In the figure, you see the frame of a lampside. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.

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Q. The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?
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Q. Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7m, find its height.
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Q.

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm (see figure). Find its
(i) Inner curved surface area.
(ii) Outer curved surface area
(iii) Total surface area

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Q. Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
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