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
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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?
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
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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?
1. 167 cu cm
2. 176 cu cm
3. 200 cu cm
4. 220 cu cm
5. None of these
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