3D Geometry: Mensuration Practice Problems: Level 02

Q.1. The area of a rectangle is four times of a square. The length of the rectangle is 80 cm and the breadth of the rectangle is 3 times that of the side of the square. What is the side of the square?
1. 40 cm
2. 30 cm
3. 45 cm
4. 60 cm
5. 20 cm
Q.2. Two small circular parks of diameters 6 m and 8 m are to be replaced by a bigger circular park. What would be the radius of this new park, in meter, if the new park occupies the same space as the two small parks (in meter)?
1. 5
2. 10
3. 15
4. 20
5. 25
Q.3. The diameter of a sphere is 10 inches. What are its volume and surface area?
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1. 50, 25
2. 10π/3, 15π
3. 500π/3, 100π
4. 75π/2, 35π2/3
Q.4. How many coins 3 mm thick and 1.2 cm in diameter should be melted in order to form a right circular cylinder, having base diameter 4 cm and height 27 cm?
1. 850
2. 950
3. 980
4. 1000
5. 900
Q.5. The length and breadth of rectangle Park is 56m and 44 m respectively. If a concrete path of width 4 m is made outside and along the length & breadth of rectangle. Find the area of concrete path.
1. 864 m2
2. 432 m2
3. 216 m2
4. 108 m2
5. None of these
Q.6. A triangle inscribed in a circle with shorter sides is 3 and 4 units long. If the longer side is the diameter, find the length of the diameter.
1. 5
2. 20
3. 30
4. 40
5. 50
Q.7. An open rectangular tank is made of concrete, the sides and base being 30 cm thick. Internally the tank is 8 m long, 4 m broad and 3 m high. Find its weight in kg, if concrete weighs 1 kg per 1000 cubic centimeter.
1. 34,548 kg
2. 44,416 kg
3. 39,416 kg
4. 40,000 kg.
5. None of these
Q8. A lawn, 40 m long and 35 m wide, is surrounded by a path 2 m wide. How many cubic metres of gravel are required to cover the path to a depth of 10 cm?
1. 11.8 cu m
2. 31.6 cu m
3. 62 cu m
4. 13.6 cu m
5. None of these
Q9. The rainwater from a flat roof 16 m long and 10 m wide is collected in a tank whose internal measurements are 2 m long, 2.4 m wide and 3 m deep. Before it started raining it was half-full and after the rain it was full. Find the height of rainfall.
1. 1.8 cm
2. 0.9 cm
3. 0.09 cm
4. 9 cm
5. 4.5 cm
Q10. A cylinder will exactly fit into a rectangular box whose internal dimensions are: length 14 cm, breadth 4 cm and height 4 cm. What is the volume of the cylinder?
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1. 167 cu cm
2. 176 cu cm
3. 200 cu cm
4. 220 cu cm
5. None of these