1. A stream, which flows at a uniform rate of 2.5 km per hour, is 20 metres wide. If the depth of a certain ferry is 1.2 m, how many litres of water will pass through the ferry in a minute?
D) None of these
The total quantity of water =
= 1000 m3 = 1000000 litres
2. The annual rainfall at a place is 43 cm. Find the weight (in metric tonnes) of the annual
rainfall on a hectare of land, taking the weight of water to be 1 metric tonne for 1 cubic metre.
D) None of these
Height of water on 1 sq m area of land annually = 43 cm
Volume of water on 10,000 sq m. area of land = × 10000 m3 = 4300 m3
Weight of water = 4300 metric ton
3. A metallic right circular cone of height 9 cm and base radius 7 cm is melted into a cuboid with two sides as 11 cm and 6 cm. What is the third side of the cuboid?
A) 5 cm
B) 6 cm
C) 7 cm
D) 9 cm
Let the third side of cuboid = x cm
Now, according to the question:
1/3 πr2h = l × b × h
⇒ 66x = 462
⇒ x = 7 cm
4. A garden is 112m long & 78 m wide. It has walking path 25m wide all around it on inside. Find the area of path ?
A) 925 m2
B) 927 m2
C) 929 m2
D) 934 m2
If path is within the garden then use this formula:
2 * B * (L + B – 2 * B)
2 * 25 (112 + 78 – 2 * 25)
= 5 * 185 = 925 m2
5. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs100 per metre it will cost the village panchayat Rs 75000 to fence the plot. What are the dimensions of the plot?
A) 274 & 100 m
B) 275 & 200 m
C) 275 & 100 m
D) None of the above
Let the common ratio between the length and breadth of the rectangular plot be x. Hence, the length and breadth of the rectangular plot will be 11x m and 4x m respectively.
Perimeter of the plot = 2(Length + Breadth)
It is given that the cost of fencing the plot at the rate of Rs 100 per metre is Rs 75, 000.
∴ 100 × Perimeter = 75000
100 × 30x = 75000
3000x = 75000
Dividing both sides by 3000, we obtain
x = 25
Length = 11x m = (11 × 25) m = 275 m
Breadth = 4x m = (4 × 25) m = 100 m
Hence, the dimensions of the plot are 275 m and 100 m respectively.