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Cube and Cuboid

1. The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm. The wood of which it is made is 1.5 cm thick. How many bricks of size 6 cm × 3 cm × 0.75 cm can be put in this box?
a) 1875               b) 2770              c) 2580           d) 2970 

= 45 × 33 × 2 = 2970 bricks.
Ans: d 

 

2. The volume (in m3) of rain water that can be collected in 1.5 hectares of ground from a rainfall of 5 cm is
a) 75         b) 750       c) 7500       d) 75000
Sol: 1 hectare = 10,000 m2
Area of the ground = 1.5 × 10000 = 15000 m2
Volume of rain water collected = 15000 × 5 × 10-2 = 150 × 5 = 750 m3
Ans: b 

 

3. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water (in litres) will fall into the sea in a minute?
a) 4,00,000            b) 40,00,000            c) 40,000            d) 4,000
Sol: Rate of flow of water = 2 × 1000/60 = 100/3 m/min 
Fall of water into the sea in one minute 
= 3 × 40 × 100/3 = 4000 m3 = 40,00,000 litre 3 
Ans: b 

 

4. Cost of covering 4 walls of a room with paper is Rs. 480. The length, breadth and height of another room is double that of this room. What shall be the cost of covering the walls of the room?
a) Rs. 960         b) Rs.1,440          c) Rs. 2,400         d) Rs.1,920
Sol: The dimensions of the new room are all twice the original one. Hence, the area shall be four times the original one. Cost shall be four times the original cost of covering the walls with paper.
Hence, cost of covering the walls of new room with paper = 4 × 480 = Rs.1,920.
Ans: d

 

5. The dimensions of a rectangular box are in the ratio of 5 : 6 : 11. If the total surface area of the box is 14798 m2, then what is the volume of the box?
a) 108114 m3            b) 113190 m3               c) 99720 m3             d) 100450 m3
Sol: Let the dimensions of the rectangular box be 5x, 6x and 11x.
Total surface area = 2(lb + bh + hl) = 2(30x2 + 66x2 + 55x2)
⇒14798 = 302x2 ⇒ x2 = 14798/302 = 49 
∴Volume of the box = 5x × 6x × 11x = 330 × x3
= 330 × 343 = 113190 m3
Ans: b

Posted Date : 23-04-2021

 

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