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Surface Areas and Volumes

Short Answer Type

1. 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, determine:

(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 m² costsर 20.

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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 र 7.50 per m².

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The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ` 10 per m2 is ` 15000, find the height of the hall. [Hint : Area of the four walls = Lateral surface area.]

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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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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 the greater lateral surface area and by how much?

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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 the greater lateral surface area and by how much?

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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?

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Long Answer Type

8. 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 र 4 for 1000 cm², find the cost of cardboard required for supplying 250 boxes of each kind.

For bigger box
l = 25 cm b = 20 cm h = 5 cm
Total surface area of the bigger box
= 2 (lb + bh + hl)
= 2[(25)(20) + (20)(5) + (5)(25)]
= 2[500 + 100 + 125] = 1450 cm²Cardboard required for all the overlap

$equals 1450 cross times 5 over 100 equals 72.5 space cm squared$

∴ Net surface area of the bigger box

= 1450 cm² + 72.5 cm² = 1522.5 cm²∴ Net surface area of 250 bigger boxes
= 1522.5 x 250 = 380625 cm²Cost of cardboard

$equals 4 over 1000 cross times 380625 equals र space 1522.50$

For smaller box

l = 15 cm b = 12 cm h = 5 cm
∴ Total surface area of the smaller box = 2 (lb + bh + hl)
= 2[(15)(12) + (12)(5) + (5)( 15)] = 2[ 180 + 60 + 75] = 630 cm²Cardboard required for all the overlaps

$equals 630 cross times 5 over 100 equals 31.5 space cm squared$

∴ Net surface area of the smaller box
= 630 cm² + 31.5 cm² = 661.5 cm² Net surface area of 250 smaller boxes = 661.5 x250 = 165375 cm²∴ Cost of cardboard

$equals 4 over 1000 cross times 165375 equals र space 661.50$

Cost of cardboard required for supplying 250 boxes of each kind
= र 1522.50 + र 661.50 = र 2184.

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Short Answer Type

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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10. The length of a hall is 20 m and width 16 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.

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